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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?

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?

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Mark M. | Mathematics Teacher - NCLB Highly QualifiedMathematics Teacher - NCLB Highly Qualif...
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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