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A balloonist is directly above a straight road 1.9 miles long that joins two towns. She finds that the town closer to her is at an angle of depression of 39 and the farther town is at an angle of depression of 38. How high above the ground is the balloon?

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The height of the balloon is 1.3 miles above the ground.

Height is a measure of vertical distance, indicating how "tall" or "high" something or someone is. A person's height, for example, is commonly measured with a stadiometer and reported in centimeters or feet and inches.

A mountain's height is often measured in meters or feet. Height in aviation is measured from the earth's surface, either above ground level (AGL) or above mean sea level (AMSL).

The Tangent trigonometric formula can be used to find the solution to this question. To determine the height of the balloon, measure the hypotenuse of the triangle formed by the two towns and the balloonist.

We may compute the length of the hypotenuse using the tangent formula. The formula is as follows:

(angle) tan = opposite/adjacent side

The opposite sides in this scenario are the two towns, and the adjacent side represents the height of the balloon.

The formula for the first town is:

tan 36° = 1.6/x

By solving for x, we can determine that the hypotenuse for the first town is 2.8 miles long.

The formula for the second town is:

tan 32° = 1.6/

By solving for x, we can determine that the hypotenuse for the second town is 2.9 miles long.

The height of the balloon can be estimated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).

The balloon reaches a height of 1.3 miles above the ground

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