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3 years ago

Best answer = brainliest

Mathematics

1 answer:

torisob [31]3 years ago

4 0

Answer:

243 in^2

Step-by-step explanation:

9*9

Surface area of a side

81*3

The sides that are painted

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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

4 0

1 year ago

Write a verbal expression for 2(n + 9)

Morgarella [4.7K]

Two times the sum of a number and nine.

8 0

4 years ago

Read 2 more answers

HELP ME PLZ!!!!! Plz!!!

Charra [1.4K]

Answer:

hi the right answer is option C.112

here's why:

$\frac{14}{50} \times 400 = 112$

4 0

3 years ago

If the volume of a cone is 12.56, and the height is 3. What is the radius of the cone? R=

Alina [70]

Answer:

you can find a radius through its volume and height. Multiply the volume by 3. For example, the volume is 20. Multiplying 20 by 3 equals 60

Step-by-step explanat

I hope to help you

5 0

2 years ago

Round off 0.043 to one significant figure

aniked [119]

Hey there :)

0.043
The first 0 before the decimal point is not significant since it is used for cosmetic purpose
The 0 after the decimal is not significant as the 0 is used to locate the decimal point
The 4 is the first nonzero integer and it counts as a significant figure

Therefore, 0.04 will be your answer rounded to 1 s.f

4 0

3 years ago

Read 2 more answers