Question

A meteorologist reads radio signals to get information from a weather balloon. The last alert indicated that the angle of depression of the weather balloon to the meteorologist was 41° and the balloon was 1,810 meters away from his location on the diagonal. To the nearest meter, how high above the ground was the balloon

Answer 1

The balloon is 1366 meters above the ground.

Step-by-step explanation:

Step 1:

The angle of depression from the balloon is 41° and the distance from the balloon to the meteorologist on the diagonal is 1,810 meters.

So a right-angled triangle can be formed using these measurements. The angle of the triangle is 41° while the adjacent side of the triangle measures x meters and the hypotenuse side of the triangle measures 1,810 meters.

We need to find the adjacent side's length of the triangle.

Step 2:

Since we have the length of the hypotenuse and need to calculate the length of the adjacent side we use the cos of the given angle.

The adjacent side of the triangle = x meters.

The hypotenuse of the triangle = 1,810 meters.

$cos\theta = \frac{adjacentside}{hypotenuse}, cos41 = \frac{x}{1810}, cos 41 = 0.7547.$

$x = 0.7547 (1810) = 1,366.007.$

So the balloon is 1,366.007 meters above from the ground. Rounding this off to the nearest meter it is 1,366 meters from the ground.