Question

A bird spots a worm on the ground. The bird is 36 feet above the ground and with a horizontal distance of 45 feet to the worm. What is the angle of the bird's view on the worm? Round your answer to the nearest hundredth.

Answer 1

Let's take a look at the situation:

We know, because of the Pythagorean theorem, that:

`\begin{gathered} d^2=45^2+36^2\rightarrow d=\sqrt[]{45^2+36^2} \\ \rightarrow d=57.63 \end{gathered}`

Thereby, using the law of sines:

`\begin{gathered} (d)/(\sin90)=(45)/(\sin a) \\ \rightarrow d\sin a=45\sin 90\rightarrow\sin a=(45)/(d) \\ \rightarrow a=\arcsin ((45)/(57.63)) \\ \rightarrow a=51.34 \end{gathered}`

The angle of the bird's view on the worm is 51.34°