Question

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?

Answer 1

We have to find how far is the bird from Amanda.

With the information given, we can draw:

We can start by finding the third angle.

The sum of the angles have to be equal to 180°, so we can find it as:

`\begin{gathered} \alpha+55\degree+63\degree=180\degree \\ \alpha=180-55-63 \\ \alpha=62\degree \end{gathered}`

Now, we can apply the Law of Sines to find the distance between Amanda (A) and the bird (B):

`(AB)/(\sin J)=(AJ)/(\sin B)`

where AJ is the distance between Amanda and Jamie and AB is the distance between the bird and Amanda.

We then can solve for AB as:

`\begin{gathered} AB=AJ\cdot(\sin J)/(\sin B) \\ AB=25\cdot(\sin63\degree)/(\sin62\degree) \\ AB\approx25\cdot(0.891)/(0.883) \\ AB\approx25.23 \end{gathered}`

Answer: 25.23 [Option A]