Answer:
[tex]\begin{gathered} x\text{ = 49}\degree \\ y\text{ = 41}\degree \end{gathered}[/tex]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:
[tex]\begin{gathered} cos\text{ x= }\frac{13}{20} \\ \\ x\text{ = }\cos^{-1}\text{ 0.65 = 49}\degree \end{gathered}[/tex]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:
[tex]\begin{gathered} sin\text{ y = }\frac{13}{20} \\ y\text{ = }\sin^{-1}\text{ 0.65} \\ .y\text{ = 41}\degree \end{gathered}[/tex]