Answer:
∠ A = 60°
Step-by-step explanation:
Using the sine ratio in the right triangle
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{13}{15}[/tex] , thus
∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{13}{15}[/tex] ) ≈ 60°
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Using the cosine ratio in the right triangle
cosR = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{RT}{RS}[/tex] = [tex]\frac{8}{10}[/tex] , thus
∠ R = [tex]cos^{-1}[/tex] ( [tex]\frac{8}{10}[/tex] ) ≈ 36.9° ( to 1 dec. places )
