Angles of elevation/depression

Question

Troy lets out 16m of string. The wind pulls the kite string tight to an angle of elevation of 48 degrees. Troy's hand is 1.3m above the ground. How high is the kite above the ground?

 

Please answer with working out

Answer 1

From Troy's hand we draw a diagonal leading up to the kite.

This diagonal is 16m in length.

From the kite (at the end of the diagonal) draw a vertical line

straight down to the same level as Troy's hand.

Draw a horizontal line from the point below the kite straight

back to the hand.

 

You now have a right triangle with a hypotenuse of length 16m.

The angle from the horizontal line and the hypotenuse is 48 degrees.

Call the length of the vertical line x.

 

Use the sine function to solve for x, then add an additional 1.3m to the answer.

 

sin A = opposite/hypotenuse

sin 48 = x/16

x = 16 sin 48

x = 11.89m

 

That is the height from the kite to the level of Troy's hand.

Add the additional 1.3m from the ground to that height for final answer.

 

The kite is 11.89 + 1.3 = 13.19m high