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 = 1,227 ft, c = 1,378 ft A) A = 65.43 ^o, B = 24.57 ^o B) A = 30.57 ^o, B = 59.43 ^o C) A = 18.91 ^o, B = 71.09 ^o D) A = 27.07 ^o, B = 62.93 ^o E) A = 57.93 ^o, B = 32.07 ^o

Question

Quizplus · Accepted Answer

Using the Pythagorean theorem, we have:
$a^2 + b^2 = c^2$
$a^2 + (1227)^2 = (1378)^2$
$a^2 = (1378)^2 - (1227)^2$
$a \approx 776.64 	ext{ ft}$
Now we can use the trigonometric ratios to find the acute angles:
$\sin A = \frac{a}{c}$
$A = \sin^{-1} \left(\frac{a}{c}ight) = \sin^{-1} \left(\frac{776.64}{1378}ight) \approx 27.07^\circ$
$\sin B = \frac{b}{c}$
$B = \sin^{-1} \left(\frac{b}{c}ight) = \sin^{-1} \left(\frac{1227}{1378}ight) \approx 62.93^\circ$
Therefore, the answer is D) A = 27.07, B = 62.93.

Using the Illustration, Find the Measure of Each Acute Angle