Question

Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. Not drawn to scale x= 6.9, y = 5.7 x=8, y = 11.3 x 11.3, y = 8 x = 5.7, y = 6.9

Answer 1

x=11.3 y=8

Explanation

here we have a right triangle, so we can use a trigonometric function to find the missing sides

so

Step 1

a)let

$\begin{gathered} angle=45\text{ \degree} \\ opposite\text{ side=8} \\ adjacent\text{ side=y} \\ hypotenuse=x \end{gathered}$

Step 2

now, fin the missing length

a) y

to find the adjacent side we can use the stan function

$tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}$

replace and solve for y( adjacent side)

$\begin{gathered} tan45=\frac{8}{y} \\ y=\frac{8}{tan\text{ 45}}=\frac{8}{1} \\ y=8 \end{gathered}$

b)x (hypotenuse)

to find the hyoptenuse we can use the sin function ,

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

replace and solve for x

$\begin{gathered} sin\text{ 45=}\frac{8}{x} \\ x=\frac{8}{sin\text{ 45}}=11.3 \\ x=11.3 \end{gathered}$

therefore, the answer is

x=11.3 y=8

I hope this helps you