Question

Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8 centimeters, and the length of A C is 6.9 centimeters. Which expressions can be used to find m∠BAC? Select three options. cos−1(StartFraction 6.9 Over 12 EndFraction) cos−1(StartFraction 9.8 Over 12 EndFraction) sin−1(StartFraction 6.9 Over 12 EndFraction) sin−1(StartFraction 9.8 Over 12 EndFraction) tan−1(StartFraction 6.9 Over 9.8 EndFraction)

Answer 1

Answer:

First and Fourth choices are correct.

Step-by-step explanation:

In the image attached you can observe the triangle described in the problem.

To find the measure of angle BAC, we just need to use trigonometric reasons. Notice that we already have all sides, so it doesn't matter which reason we use.

$cos(\angle BAC)=\frac{6.9cm}{12cm} =0.575\\\angle BAC = cos^{-1} (0.575) \approx 55\°$

This means the first choice is correct.

$sin(\angle BAC)=\frac{9.8cm}{12cm}\\\angle BAC = sin^{-1} (\frac{9.8cm}{12cm})$

The fourth choice is correct.

$tan(\angle BAC)=\frac{9.8cm}{6.9cm}\\\angle BAC = tan^{-1}(\frac{9.8cm}{6.9cm})$

The last choice is not correct, because that option is showing the inverse of the tangent function.

Answer 2

Answer:

tan−1(StartFraction 6.9 Over 9.8 EndFraction)

Step-by-step explanation:

tan−1(StartFraction 6.9 Over 9.8 EndFraction)

tan = opp/adj = 9.8/6.9

tan -1 = 1 / tan = 1 / (9.8 /6.9) = 6.9 /9.8