Answer:
x = 38.7°
y = 51.3°
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are the legs.
Choosing any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
In the right triangle shown in the picture, we are given the length of the two legs and it's required to find the acute angles x and y.
The trigonometric ratio that relates both legs is the tangent, defined as follows:
[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
Let's use the angle x:
[tex]\displaystyle \tan x=\frac{8}{10}=0.8[/tex]
Now we use the calculator to find the angle whose tangent is 0.8:
[tex]x=\arctan 0.8[/tex]
x = 38.7°
Now we use angle y:
[tex]\displaystyle \tan y=\frac{10}{8}=1.25[/tex]
[tex]y=\arctan 1.25[/tex]
y = 51.3°
