chau is flying two kites. He has 100 feet of string out to one kite and 115 feet out to the other kite. The angle formed by the 2 strings is 34 degrees. Find the distance between the kite

Question

chau is flying two kites. He has 100 feet of string out to one kite and 115 feet out to the other kite. The angle formed by the 2 strings is 34 degrees. Find the distance between the kite

Answer 1

Hi Badr,

When you get a word problem like this, I recommend starting by drawing it out. If you draw it, you get a triangle. One side is 100, one side is 115, and the angle between those two sides is 34 degrees.

Next, figure out what the question wants you to solve. The question asks for the distance between the two kites, let's call it c, which is the third side of the triangle (and the side that is opposite the 34 degree angle).

When we know 2 sides and their included angle, we can find the 3rd side of any triangle using the Law of Cosines, also known as the Cosine Rule:

c² = a² + b² − 2ab*cos(C)

We can plug in 100 for a and 115 for b (our two known sides), and 34 degrees for C (the included angle). Solving, we get:

c² = 100² + 115² − 2(100)(115)*cos(34)

c² = 100² + 115² − 2(100)(115)*cos(34)

c² = 1000 + 13225 − (23000)*(0.829)

c² = 23225 − 19067

c² = 4158

c = 64.48 feet

And you have your answer! The distance between the kites is 64.48 feet. I hope this helps, and good luck with your work!

Best,

Stephanie