# Chapter 10 - Geometry - 10.6 Right Triangle Trigonometry - Exercise Set 10.6 - Page 666: 26

$A \approx 10^o$

#### Work Step by Step

RECALL: In a right triangle, $\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}} \\\cos{A} = \dfrac{\text{length of adjacent side}}{\text{length of hypotenuse}} \\\tan{A} = \dfrac{\text{length of opposite side}}{\text{length of adjacent side}}$ Use the sine formula to obtain: $\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}} \\\sin{A}=\dfrac{11}{65}$ Use the inverse sine function of a scientific calculator to obtain: $A = \sin^{-1}{\frac{11}{65}} \\A = 9.743097377^o \\A \approx 10^o$

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