Triangle ΔABC has side lengths of a = 18, [tex]b=18\sqrt{3}[/tex] and c = 36 inches.

Part A: Determine the measure of angle A

Part B: Show how to use the unit circle to find tan A

Part C: Calculate the area of ΔABC.

Answers

Answer 1

The measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

What is the law of cosine?

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle B=\cos^{-1}\left(\dfrac{a^2+c^2-b^2}{2ac}\right) \\\angle C=\cos^{-1}\left(\dfrac{a^2+b^2-c^2}{2ab}\right)[/tex]

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

Triangle ΔABC has side lengths of a = 18, b=18√3  and c = 36 inches.

Part A: Determine the measure of angle A

Put the value, in the cosine law, the measure of angle A.

[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle A=\cos^{-1}\left(\dfrac{(18\sqrt{3})^2+36^2-18^2}{2(18\sqrt{3})(36)}\right) \\\angle A=0.5236\rm\; rad\\\angle A=30^o\rm\; degree\\[/tex]

Part B: Show how to use the unit circle to find tan A

Using the chart of unit circle, the value of tangent A can be found out. The tangent A is,

[tex]\tan A=\tan 30^o\\\tan A=\dfrac{1}{\sqrt{3}}[/tex]

Part C: Calculate the area of ΔABC.

Use the following formula to find area of ΔABC.,

[tex]A=\dfrac{ab.\sin C}{2}\\A=\dfrac{18\times18\sqrt{3}.\sin C}{2}\\A=280.6\rm\; in^2[/tex]

Thus, the measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

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Related Questions

please help this is urgent!!

Answers

Answer:

x=37 and scalene or right triangle

Step-by-step explanation:

Answer:

37°

Step-by-step explanation:

Any Triangle his total angles = 180

then: 53 + 90 + X = 180

then: X= 180 - (90+53)

= 37

Can you crack the code?
One number is
correct and placed
well
2
6
5
Nothing is right
3
8
7
One number is correct but wrongly placed
2
3
4
Two numbers are correct but wrongly placed
4
7
1
The numeric logic has a digit of
?
?
?

Answers

Answer:

1,2,4 is the correct answer

hope it'll help you out

Question 13
You deposit $8,400 in an account earning 3.6% interest compounded monthly.
a. How much will you have in the account in 20 years?
b. How much interest will you earn?

Answers

Answer:

A = $17,238.65

I (interest) = $8,838.65

Step-by-step explanation:

Using the formula A = P(1 + r/n)^nt

A = $17,238.65

A = P + I where

P (principal) = $8,400.00

I (interest) = $8,838.65

First, convert R as a percent to r as a decimal

r = R/100

r = 3.6/100

r = 0.036 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 8,400.00(1 + 0.036/12)^(12)(20)

A = 8,400.00(1 + 0.003)^(240)

A = $17,238.65

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $8,400.00 at a rate of 3.6% per year compounded 12 times per year over 20 years is $17,238.65

use this dataset for the next three questions: 5, 10, 12, 4, 6, 11, 13, 5 1. Calculate the mean. 2 Ultimate Medical Academy.
calculate the mean​

Answers

Answer:

11.8

Step-by-step explanation:

5 + 10 + 12 + 4 + 6 + 11 + 13 + 51= 118

The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.

Count = 10

Sum = 118

Average = Sum / Count

118/10= 11.8

Write the equation of the line which passes through the point (6, 1) and
is perpendicular to the line y = 3x - 2:

Answers

Answer : Look at the right hand side of the page y = 1/3x + 3

All four triangles are similar, and two of the triangles are also congruent to each other. Drag the correct unit side lengths and angle measures to te corresponding boxes. Note that some values may be approximate.

Answers

Answer:

Step-by-step explanation:

I get everything correct

Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.

Answers

The number that indicates the extent of a region on a plane or a curved surface is known as area. The total surface area of this triangular prism is 1,782 cm².

What is the area?

The number that indicates the extent of a region on a plane or a curved surface is known as area. The area of a plane region or plane area refers to the area of a form or planar lamina, whereas the area of an open surface or the border of a three-dimensional object is referred to as surface area.

The given figure has two rectangles and two triangles, therefore, the total surface area can be written as,

[tex]\rm Total\ Surface\ Area =\text{Surface area of rectangle1} + \text{Surface area of rectangle2} + (2 \times \text{Surface area of triangle})\\[/tex]

Substitute the dimensions we will get,

[tex]\rm Total\ Surface\ Area =( 25 \times 30)+ (24 \times 25) + (2 \times \dfrac12 \times 18 \times 24)[/tex]

                              [tex]\rm = 750+600+432\\\\=1,782\ cm^2[/tex]

Hence, the total surface area of this triangular prism is 1,782 cm².

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6x -3y -15 = 0 please solve for me

Answers

Step-by-step explanation:

Add 3y to both sides

6x-3y- 15 + 3y =0+3y

Simplify

6x- 15 =3y

Add 15 to both sides

6x-15 + 15 =3y + 15

Simplify

6x =3y+ 15

Divide both sides by6

6x/6= 3y/6+ 15/6

x=y+5/2

Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
15% tip on a bill of $41.58 The amount of the tip is approximately $

Answers

Answer:

Approximately $6.24

Step-by-step explanation:

You have to multiply 41.58 by 0.15 (basically 15%) and you have your answer.

Find the side length of a square with area 16/49 square inches

Answers

Answer: the correct answer is S= 4/7 inches.

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Answer:

use sine or cosine rule

Step-by-step explanation:

that's the answer by using the sine rule

Answer:

Step-by-step explanation:

Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis.
y = 3 − x

Answers

The volume of the solid generated by revolving the plane region y=3−x about the y-axis is 9π cubic units.

What is integration?

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a function:

y = 3 - x

From the graph:

Shell radius = y

Height = 3 - y

From the shell method, we can write the integral as follows:

[tex]\rm Volume =2\pi\int\limits^0_{-3} {y(3-y)} \, dy[/tex]

[tex]\rm Volume =2\pi\int\limits^0_{-3} {(3y-y^2)} \, dy[/tex]

After solving the above definite integral, we will get volume:

Volume = 9π cubic units

Thus, the volume of the solid generated by revolving the plane region y=3−x about the y-axis is 9π cubic units.

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NEED THIS ASAP
Which statement describes (²) ?
n=1
The series diverges because it has a sum of 1.
O The series converges because it has a sum of 1.
O The series converges because it has a sum of 4.
The series diverges because it does not have a sum.

Answers

Answer:

option b

please mark me as brainliest

Answer: the series converges because it has a sum of 1 (b)

Step-by-step explanation:

bec i said so

If x is 6 and y is -2 what’s the value of yx

Answers

Answer:

-12

Step-by-step explanation:

(6)(-2)= -12

6 multiply -2 equals 12.

A circular flower garden surrounds a sculpture on a square base as shown. What is an expression for the area of the flower garden?
The number from the center of the square is 6x and the flower garden area is 4x

Answers

The given object is made up of circle and squares. The expression for the area of the flower garden is 4π²(9π - 4)square units

Area of composite object

The given object is made up of circle and squares. To find the area of the garden, we wil use the expression

Area of the garden = area of circle - area of square

Find the area of circle

Area = πr²

Area = π(6π)²

Area pf circle = 36π³ square units

For the square

A = length * length

A = 4²π²

A = 16π²square units

Take the difference

D =   36π³ - 16π²

D =4π²(9π - 4)square units

Hence the expression for the area of the flower garden is 4π²(9π - 4)square units

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Answer: (pi * r^2) - (6x*4x)

Step-by-step explanation:
Since the formula of the area of a circle is pi * r^2 and the area of a square is base* height or in this case 6x*4x the answer is: (pi * r^2) - (6x*4x). The reason we subtract is because your trying to find the area of the square inside the circle.

Write the algebraic expression that matches each graph.
(WILL GIVE BRAINLIEST!)

Answers

Answer:

y=11

Step-by-step explanation:

Find the volume of this shape. Show work and round to the nearest hundredth pls.

Answers

Answer:

V = 150.80 cu.ft.

Step-by-step explanation:

shape is a cone

[tex]V=\frac{1}{3} \pi r^{2} h[/tex]

[tex]r=8/2=4ft[/tex]

[tex]h=9ft[/tex]

Then:

[tex]V=\frac{1}{3} \pi (4)^{2} (9)=48\pi =150.80cu.ft[/tex]

Hope this helps

A whole number is squared. The result is between 200 and 260. The number is between:
A) 10 and 11
B) 15 and 16
C) 13 and 14

Answers

Answer:

B

Step-by-step explanation:

b is correct

Ali and Keesha found a sale in a sporting goods store. Ali spent $33 on 2 pair of shorts and 3 packages of socks. Keesha spent $27 on 1 pair of shorts and 5 packages of socks. How much does one of each item cost?

Answers

Answer: shorts cost $12 and socks cost $3

Step-by-step explanation:

what is the simplest form of 2/3 - 1/4 =

Answers

Answer:

I got 5/12

Step-by-step explanation:

Hope this helped

ANSWER

The answer will be

Step-by-step explanation:

5/2=0•416666667

28 out of 35 students in ms. baileys class have older siblings. what percent of the class has older siblings

Answers

Answer:

80%

Step-by-step explanation:

We can get the percent value of the amount of students who have older siblings by diving 28 by 35.

28 / 35 = 0.8

We can convert this decimal into a percentage, giving us 80%.

Therefore, we know that 80% of the students in Ms. Bailey's class have siblings.

Let Vector f = LeftAngleBracket 4, 3, 7 RightAngleBracket. and Vector g = LeftAngleBracket negative 1, 0, 2 RightAngleBracket. . Which graph shows Vector f + vector g. ?

Answers

Vectors simply means a quantity that has both magnitude and direction but not position e.g acceleration.

What is a vector?

Your information is incomplete as the graphs aren't given. Therefore, an overview of vectors will be given.

In this case, vectors simply means a quantity that has both magnitude and direction but not position e.g acceleration, velocity, etc.

A vector can also be an element of the vector space. The direction is typically equal to the angle formed with the x-axis.

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Question 7 of 10
How many different roots does the polynomial function, y = (x - 2)(+3)
have?
O A. 4
B. 3
O c. 2
O
D. 1
SUBMIT

Answers

c. 2

you should just get an app on ur phone its easier than asking here

Two different roots the given polynomial function have. Therefore, option C is the correct answer.

What is the solution of a quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given equation is y=(x-2)(x+3)

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

Here, (x-2)(x+3)=0

(x-2)=0 and (x+3)=0

x=2 and x=-3

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

How many different roots does the polynomial function, y = (x - 2)(x+3)?

A. 4

B. 3

C. 2

D. 1

The diameter of a circle is 20 m. Find the circumference to the nearest tenth.​

Answers

ANSWER: 62.83 m


explanation- c=2 pie

d=2r

c=pie d=pie • 20 = 62.83185 m

Answer:

about 62.8 meters

Step-by-step explanation:

[tex]c = 20\pi = 62.8[/tex]

What is the volume of this object?
__u3

Answers

Answer:

15u³

Step-by-step explanation:

To find volume ↓

Volume

= length × width × height

= 2u × 2½u × 3u

= 15u³

Hope this helps =)

If the radius of the circle below is 12 feet, find the area of the shaded region.

Answers

If the radius of the circle below is 12 feet is given then the area of the circle would be 452.16 ft square.

What is the area of the circle?

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = [tex]\pi r^{2}[/tex]

If the radius of the circle below is 12 feet is given then

The area of the circle = [tex]\pi r^{2}[/tex]

 [tex]\pi 12^{2} \\\\3.14 \times 144\\\\452.16[/tex]

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NOTES
Lucia and Jack are training for a marathon. Lucia started the first day by running 2 miles and adds 0.25 mile to her distance every day, Jack
started the first day by running 0.5 mile and adds 0.5 mile to his distance every day. If both continue this plan, on what day will Lucia and
Jack run the same distance?

Answers

Answer:

Day 3

Step-by-step explanation:

2+0.25+0.25=2+0.50=2.50

0.5+0.5+0.5=2+0.5=2.5=2.50

they both run 2.50 miles on day three

The fox population in a certain region has an annual growth rate of 5 percent per year. It is estimated that
the population in the year 2000 was 28400.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)

Answers

Answer:

See below

Step-by-step explanation:

population =  28400* ( 1+.05)^t     t = years past 2000

8 years from 2000     pop = 28400(1.05)^8= 41 960 foxes

The sum of two fractions is 2/3.
One fraction is 1/2.
What is the other fraction?

Answers

Answer:

0.5/3

Step-by-step explanation:

1/2 can be turned into 2/4, which means that to be 1/3, it has to be 1.5/3. 1.5/3 + 0.5/3 equals 2/3.

The other fraction would be 1/6.

A pizza dough recipe has a ratio of 5 cups of flour to 2 cups of water. There are ?
cups of flour per cup of water

Answers

Answer:

2.5 cups of flour per cup of water.

Step-by-step explanation:

We can divide the entire recipe by two, to get the amount of flour to 1 cup of water.

5/2 = 2.5

2/2 = 1

Therefore, 2.5 cups of flour needs 1 cup of water.

Answer:

There are 2.5 cups of flour per cup of water

Step-by-step explanation:

Step 1:  Find the ration

Cups of Flour : Cups of Water

5 : 2

2.5 : 1

Answer:  There are 2.5 cups of flour per cup of water

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