Answer:
1) x ≅ 51.34°
2) y ≅ 38.66°
Step-by-step explanation:
In the right triangle given in the figure
∵ The triangle has a right angle
∴ Angles x and y are acute angles and the sum of their measures is 90°
→ By using the trigonometry function tan
∵ tan(x) = opposite side to x/adjacent side to x
∵ The opposite side to x = 10
∵ The adjacent side to x = 8
→ Substitute them in the rule above
∴ tan(x) = [tex]\frac{10}{8}[/tex] = [tex]\frac{5}{4}[/tex]
→ Use the inverse of tan to find x
∵ x = [tex]tan^{-1}[/tex]([tex]\frac{5}{4}[/tex])
∴ x = 51.34019175
∴ x ≅ 51.34°
∵ x + y = 90°
∴ 51.34 + y = 90
→ Subtract 51.34 from both sides
∴ y ≅ 38.66°
