Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. b = 14.6 m, c = 16.1 m A) A = 20.8 ^o, B = 69.2 ^o B) A = 24.9 ^o, B = 65.1 ^o C) A = 67.6 ^o, B = 22.4 ^o D) A = 16.4 ^o, B = 73.6 ^o E) A = 70.1 ^o, B = 19.9 ^o

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem, we can solve for the length of side a:
a² + b² = c²
a² + (14.6 m)² = (16.1 m)²
a² = (16.1 m)² - (14.6 m)²
a² = 98.41 m²
a = 9.92 m

To find the measure of angle A, we can use the inverse tangent function:
tan(A) = opposite/adjacent
tan(A) = 9.92 m/14.6 m
A = tan⁻¹(9.92/14.6)
A = 24.9°

To find the measure of angle B, we can use the fact that the sum of the measures of the angles in a triangle is 180°:
B = 180° - 90° - 24.9°
B = 65.1°

Therefore, the best choice is B, which gives the measures of angle A as 24.9° and angle B as 65.1°.

Using the Illustration, Find the Measure of Each Acute Angle