Ivanna is flying two kites She has 100 feet of string out to

Ivanna is flying two kites. She has 100 feet of string out to one kite and 118 feet out to the other kite. The angle between the strings is 36 degree as shown in the figure below. Find the distance between the kites. Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth of a foot.

Solution

Using law of cosine

a^2=b^2 + c^2 -2bc cos A

here b=100,c =118 and <A=36

Therefore a^2=100^2 + 118^2 - 2*100*118 cos 36

a^2= 10000+ 13924- 23600 cos 36

a^2= 23924 -

a^2= 23924- 19092.80107

a^2= 4831.1989

taking sqrt both sides

sqrt a^2=sqrt 4831.1989

a= 69.5068

THerefore the distance between the two kites is 69.5068 foot