A hot-air balloon is flying at an altitude of 2206 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 27degrees, how far is the house from the pilot?

The angle of depression is 27 degrees, and the side opposite the angle is the altitude of the balloon (2206 feet). The side adjacent to the angle is the horizontal distance from the balloon to the house.

Let's call the horizontal distance from the balloon to the house "x". Then, we can set up the following equation:

tan(27 degrees) = 2206 feet / x

To solve for x, we can rearrange the equation:

x = 2206 feet / tan(27 degrees)

Using a calculator, we can find the value of the tangent of 27 degrees:

tan(27 degrees) ≈ 0.5095

Now, we can plug this value into the equation to find the horizontal distance from the balloon to the house:

x ≈ 2206 feet / 0.5095 ≈ 4330.7 feet

So the house is around 4330.7 feet from the pilot in the balloon.

A​ hot-air balloon is flying at an altitude of 2206 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 27degrees​, how far is the house from the​ pilot?

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A hot-air balloon is flying at an altitude of 2206 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 27degrees, how far is the house from the pilot?