Question

1.

Answer 1

The clouds are 226.68 meters above the spotlight.

Step-by-step explanation:

Step 1:

The angle measuring device is 65 meters from the spotlight and the angle of elevation from the ground to the spot of light is 74°.

So a right-angled triangle can be formed using these measurements. The angle of the triangle is 74° while the opposite side of the triangle measures x meters while the adjacent side of the triangle measures 65 meters.

We need to calculate the opposites side's length of the triangle.

Step 2:

Since we have the adjacent side's length and need to calculate the opposite side's length we use the tan of the given angle.

The opposite side of the triangle = x meters.

$\tan \theta = \frac{oppositeside}{adjacentside} = \frac{x}{65}.$

$tan 74 = 3.487, x = 3.487(65) = 226.07.$

So the spot of light is 226.07 meters above from the spotlight.