Question

What is the angle of elevation of the sun if a 55 foot tall flag pole casts a 16 foot long shadow?

Answer 1

check the picture below.

make sure your calculator is in Degree mode.

Answer 2

73.8 degrees.

Explanation:

Please find the attachment.

Let x represent angle of elevation of the sun.

We have been given that a 55 foot tall flag pole casts a 16 foot long shadow.

We can see from our attachment that flag and shadow forms a right triangle with respect to ground, where side with length 55 ft is opposite side and side with length 16 ft is adjacent side.

We know that tangent relates opposite side of right triangle with adjacent side.

`\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

Upon substituting our given values, we will get:

`\text{tan}(x)=(55)/(16)`

Now, we will use inverse tangent to solve our problem as:

`x=\text{tan}^(-1)((55)/(16))`

`x=73.779806^(\circ)`

`x\approx 73.8^(\circ)`

Therefore, the angle of elevation is approximately 73.8 degrees.