Question

Lance, Rachael, and Jamie are playing catch. Lance throws the ball to Rachael, Rachael to Jamie, and Jamie back to Lance. The angle formed at Rachael's position measures 90°. The distance from Lance to Rachael is 45 feet, and the angle formed at Lance's position measures 55°. Lance is trying to determine the other measures created by their positions. Give each measurement rounded to the nearest thousandth of a foot.

Answer 1

The shape formed by the three is a right triangle because the angle formed at Rachael's position is 90°. 

The known values are 90°, 55° and 45 ft.

Since the sum of all angles in a triangle is 180 degrees, we can easily solve for the angle formed by Jamie: 180°-90°-55° = 35°.

For the distance between Jamie and Lance (JL): cos 55° = 45/JL
JL = 78.455 feet.

For the distance between Jamie and Rachael (JR): tan 35° = 45/JR
JR = 64.267 feet.