Btw sry I know my handwriting sucks
so I'm guessing they want us to assume that OKM is splitting the right angle perfectly in half otherwise they would label it and so therefore that is why I'm splitting them in half (half of ninety is forty five) also just thought I'd add a pic showing the angles. I hope this helps

7 0

3 years ago

worty [1.4K]

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.

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