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)((l)/(h))`

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

`\alpha=\cot ^(-1)((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°.