Question

Solve for the hypotenuse and then determine the ratios below (show all work)

Answer 1

hypotenuse=29

`\sin x=(20)/(29)`

`\cos y=(20)/(29)`Step-by-step explanation

Step 1

a) hypotenuse

to find the hypotenuse we can use the Pythagorean theorem ,it statse that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)

so

`\begin{gathered} 21^2+20^2\text{= hypotenuse}^2 \\ 441+400=\text{ hypotenuse}^2 \\ 841=\text{hypotenuse}^2 \\ taking\text{ the square root in both sides} \\ √(841)=√((hypotenuse)^2) \\ 29=hypotenuse \end{gathered}`

so

hypotenuse=29

Step 2

now, sin x

the sin of an angle is the ratio of the opposite side ( the one in front of the angel) to the hypotenuse

`\sin\theta=\frac{opposite\text{ side}}{hypotenuse}`

hence, replace

`\sin x=(20)/(29)`

Step 3

finally, cos of y

the cos of an angle is the ratio of the adjancent side( the side the makes the angle) to the hypotenuse

`cos\theta=\frac{adjacent\text{ side}}{hypotenuse}`

so,replace

`\cos y=(20)/(29)`

I hope this helps you