Answer:
- cos ⁻¹ [6.3/9.8] . . . second choice, and
- sin ⁻¹ [7.5/9.8] . . . last choice.
Step-by-step explanation:
The little red square indicates that the angle C measures 90°, which means that ABC is a right triangle.
The opposite side to angle C is the hypotenuse of the triangle. Then, the hypotenuse measures 9.8 in.
The requested measure, m ∠ ABC, is the measure of the angle B.
With respect to angle B you have:
Thus, the trigonometric ratios for angle B are:
- cos B = adjacent leg / hypotenuse = 6.3 in / 9.8 in = 6.3 / 9.8
- sin B = opposite leg / hypotenuse = 7.5 in / 9.8 in = 7.5 / 9.8
Finally, to find the measures of angle B, you just need to find the inverse functions, which are:
- cos ⁻¹ [6.3/9.8] . . . second choice, and
- sin ⁻¹ [7.5/9.8] . . . last choice.