Question

A flagpole that is 32 feet tall casts a 67-foot shadow. What is the angle, markedwith an x on the diagram, that the sun hits the flagpole? Round to the nearestdegree, and enter the number only.

Answer 1

We will solve as follows:

*We will use the following expressions:

$l=h\cot (\alpha)$$\alpha=\cot ^{-1}(\frac{l}{h})$

[Thit these we will find the angle on the ground and using this we will determine x]

$\alpha=\cot ^{-1}(\frac{67}{32})\Rightarrow\alpha=25.53$

So, we have that the other angle is 25.53. Now, since we know that the sum of all internal angles of a triangle adds 360°, and we already have two sides, we find the value of x as follows:

$90+25.53+x=360\Rightarrow x=244.47$

So, the angle of x is approximately 244°.