Answer to Question #153926 in Trigonometry for Morayo

Question

A 100 foot wire is extended from the ground to the top of a 60 foot pole, whish is perpendicular to the level ground. Find to the nearest degree, the measure of the angle that the wire makes with the ground.

Answer 1

Here in the image, AB is the 60ft tall pole and AC is the 100ft tall wire.

As $\angle$ ABC is $90^o$ , we use trigonometry:

$$sin\theta=\frac{AB}{AC}=\frac{60ft}{100ft}=\frac{60}{100}=\frac{3}{5}$$

Therefore we have,

$$sin\theta=\frac{3}{5}\\ \Rightarrow \theta=sin^{-1}(\frac{3}{5})\\ \Rightarrow \theta\approx0.6435\approx36.8698^o$$

Therefore the angle that the wire makes with the ground is $36.8698^o.$