Question

Instructions: Find the measures of the unknown angles in thetriangle shown. Round answers to the nearest degree.

Answer 1

`\begin{gathered} x\text{ = 49}\degree \\ y\text{ = 41}\degree \end{gathered}`

Step-by-step explanation:

Here, we want to get the values of the angles marked x and y

for x:

We do not have any angle facing x

However, we have the length of the hypotenuse (the longest side and the side that faces the right angle) which is 20)

We have the length of the adjacent which is 13

The trigonometric identity to use here is the cosine

It is the ratio of the length of the adjacent side to that of the hypotenuse

Mathematically:

`\begin{gathered} cos\text{ x= }(13)/(20) \\ \\ x\text{ = }\cos^(-1)\text{ 0.65 = 49}\degree \end{gathered}`

for y:

We have an angle facing it which means 13 is the opposite.

We already have the hypotenuse

The trigonometric identity to use is the sine

It is the ratio of the length of the opposite to that of the hypotenuse

We have that as:

`\begin{gathered} sin\text{ y = }(13)/(20) \\ y\text{ = }\sin^(-1)\text{ 0.65} \\ .y\text{ = 41}\degree \end{gathered}`