Trigonometry word problem

Question

At 6 a.m., the angle of elevation of the sun from the horizon is 0 degrees. At noon, the angle of elevation of the sun is 87 degrees. At some time before noon, a flagpole 50 feet tall casts a shadow 24 feet 9 inches long. To the nearest minute, what is the time? Explain your work. Assume the angle of elevation of the sun increases at a constant rate. Draw a picture.

Answer 1

The sun takes 6 hours to rise 87 degrees, so it rises 87/6 = 14.5 degrees per hour.

Now calculate the angle of the sun in the sky. Use 24.75 ft length of shadow as horizontal side of right triangle, and 50 ft height of pole as vertical side of triangle. Tan θ = 50/24.75 = 2.02; Tan^-1 2.02 = 63.66 degrees.

Hours since sunrise = 63.66/14.5 = 4.39 h.

So the time is 6 AM + 4 h 23 m = 10:23 AM