Trigonometry Word Problem

Question

A tennis player hits an overhead smash 35ft from the net. If the ball is hit 10.5 ft off the ground and just clears the net at a height of 3 ft, how far from the net and at what angle will the ball strike the ground?

Answer 1

Draw a large right triangle and a small right triangle at the end of the large right triangle to create similar triangles

We have 10.5 : 3 as 35:x

write as fractions

10.5 /3 = 35/x

cross multiply

105 = 10.5 x therefore x =10 (this is how far past the net the ball hits)

the ball hits the ground at ARCTAN(10.5/45) = 13.134 degrees

ARCTAN is the inverse tan button on your calculator