Question

In the figure, AC = 15 ft, m∠ABC = 60°, m∠ADC = 45°, and m∠AEC = 30°. Find each of the following measures. Show your work or explain your reasoning.

Answer 1

a) BC = 8.66 feet

b) AD = 21.2134 feet

c) EC = 25.9785 feet

Explanation:

a)

To find the length of BC, we just need to use the tangent relation of the angle ABC, where the opposite side is the length of AC and the adjacent side is the length of BC:

tangent(60) = AC / BC

1.7321 = 15 / BC

BC = 15 / 1.7321 = 8.66 feet

b)

To find the length of AD, we just need to use the sine relation of the angle ADC, where the opposite side is the length of AC and the hypotenusa is the length of AD:

sine(45) = AC / AD

0.7071 = 15 / AD

AD = 15 / 0.7071 = 21.2134 feet

c)

Similarly to the procedure in letter a), to find the length of EC, we just need to use the tangent relation of the angle AEC, where the opposite side is the length of AC and the adjacent side is the length of EC:

tangent(30) = AC / EC

0.5774 = 15 / EC

EC = 15 / 0.5774 = 25.9785 feet