Calvin Butterball is lying on the ground and spots a hot air balloon at an angle of elevation of 28 The distance from Calvin to the hot air balloon is 850 feet. How high in the air is the balloon?

 approximately 399 feet

The more accurate value is 399.050828368008 feet, but this value is still approximate.

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Work Shown:

Refer to the diagram below.

To find x, we'll use the sine rule

sin(angle) = opposite/hypotenuse

sin(28) = x/850

850*sin(28) = x

x = 850*sin(28)

x = 399.050828368008 ...... make sure your calc is in degree mode

x = 399

I'm rounding to the nearest whole number since the given values (28 and 850) are also whole numbers. If your teacher provides other rounding instructions, then be sure to follow that.

The hot air balloon is approximately 399 feet off the ground.