SOLUTION: the string of the kit is taut and makes an angle of 54�20' with the horizontal. Find the approximate height of the kite above level ground if 28m are out and the end of the string

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Question 691336: the string of the kit is taut and makes an angle of 54�20' with the horizontal. Find the approximate height of the kite above level ground if 28m are out and the end of the string is held 1.5m above the ground.
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
It may help to draw a diagram. Draw a right triangle with legs that are horizontal and vertical.

Label the acute angle formed by the horizontal leg and the hypotenuse as "A". Angle A is 54 degrees and 20 minutes (or just degrees since 20 minutes is 1/3 of a degree).

Label the hypotenuse as 28m. We are interested in finding the vertical leg. Let's call the vertical leg x.

The vertical leg is opposite to angle A and the side we know is the hypotenuse. So we will use a Trig function that has opposite and hypotenuse in its ratio.

That would be sin. So:

Multiplying both sides by 28 we get:

Point A is where the end of the string is held. We are told that this is 1.5m above the ground. So the total height of the kite is the vertical leg plus the 1.5:

This is an exact expression for the answer. If you want or need a decimal approximation then you will need a calculator (or calculator program on your computer). Many calculators allow you to enter whole expressions. If yours is one of these then you could just enter:

Notes:
(Most calculators don't handle mixed numbers well.)
You should get a number that is a little more than 24. If you don't, then check to make sure your calculator is working in degree mode.