Math word problem using law of sines

Question

a 12-meter flagpole casts an 18-meter shadow down a slope when the angle of elevation of the sun is 50 degrees.  Find the angle of the slope from the horizontal

Answer 1

See of this picture describes the problem, and the solution.

http://hwmath.net/solutions/angle-elevation.jpg

 

Whenever you have a trig problem, draw a triangle. In this case, make sure the triangle models the problem. Figure out what you can calculate from the information that is given, then see if you can answer (or calculate the answer) from that.

Answer 2

Draw and label a diagram.

 

A is the top of the flagpole.

B is the base of the flagpole.

C is the tip of the shadow.

 

sin ∠CAB / 18 = sin ∠ACB / 12

0.64 / 18 = sin ∠ACB / 12

0.36 = sin ∠ACB / 12

0.42 = sin ∠ACB

sin^-1 0.42 = ∠ACB

24.8 = ∠ACB

 

∠CBA = 115.2

 

The angle of the slope from the horizontal is 25.2°