Question

A man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52°. How far away is the man from the spot directly under the kite?

Answer 1

the man is 61.6 ft away from the spot directly under the kite.

Explanation:

in order to find the bottom length which is b we need to First find the height of this right angle triangle.

to find the height we need to use sin:

sin 52° = X/100

sin 52° * 100 = h

h= 78.8 ft

next we can find b which is the base of the triangle.

a^2+b^2=c^2

100^2 +b^2 = 78.8^2

100^2 -78.8^2 = b^2

b^2= 3790.56

b= √3790.56

b= 61.6 ft

therefore the man is 61.6 ft away from the spot directly under the kite.

Answer 2

61.57 ft

Explanation:

Look at the picture. You need to find the base value.

so we can sue the cosine formula here.

cos x° = adjacent / hypotaneous

cos 52 ° = adj / 100

adjacent = 100 cos 52°

=61.57 ft