elevation to the crossbar 24 degrees.forward 6 yards closer and AOE is 38 degrees. How far is nick from the goal posts and how high is the crossbar?

Question

Nick is standing on the football field looking at the goal posts, getting ready to kick a field goal. He measures the angle of elevation to the crossbar and gets 24 degrees. He then moves straight forward 6 yards closer and now his angle of elevation is 38 degrees. How far is nick from the goal posts and how high is the crossbar?

Answer 1

Draw and label a diagram.

A is Nick's first position

B is 6 yards closed to the posts.

C is the base of the posts

D is the top of the posts

 

tan 24° = DC / (6 + BC)

(6 + BC) tan 24° = DC

 

tan 38° = DC / BC

(BC) tan 38° = DC

 

Set two left sides equal and solve for BC

Use BC to calculate BC