Question

As shown in the figure below, Mary is standing 31 feet from the base of a leaning tree. The length of the tree is 57 feet. The angle of elevation from where Mary is standing to the top of the tree is 73 degrees. Find the angle, theta, that the tree is leaning. Round your answer to the nearest tenth of a degree.

Answer 1

Answer:

the measure of Ф = 75.7°

Step-by-step explanation:

we will use the sin rule to find the measure of Ф

At first we will find the angle opposite to the side of length 31

∵ 180° - 73° = 107°

∴ the measure of the angle opposite to the side of length 31 is 107° - Ф

∵ sin(107° - Ф)/31 = sin(73°)/57

∴ sin(107° - Ф) = [31 × sin(73°)] ÷ 57

∴ sin(107° - Ф) = 0.52009

∴ (107° - Ф) = $sin^{-1}(0.52009)$

∴ (107° - Ф) = 31.338°

∴ 107° - 31.338° = Ф

∴ Ф = 75.662 ≅ 75.7°