A flag pole stands at a right angle to the horizontal at the bottom of a slope.The slope has an incline of 8 degrees with the horizontal.The flag pole casts a 2

Question

A flag pole stands at a right angle to the horizontal at the bottom of a slope.The slope has an incline of 8 degrees with the horizontal.The flag pole casts a 20 meter long shadow up the slope.The angle of elevation of the sun is 17 degrees.Determine the height of the flagpole

Answer 1

THIS IS A GOOD PROBLEM--someone voted it thumbs down but that's terrible!

 

This problem has a variation on the usual length-of-shadow problem in that the shadow is on an incline, so right triangle trigonometry doesn't cut it.

 

Draw the vertical flagpole TB (points top & bottom, respectively) and place the sun upward and to the left of point T.

Extend a ray of sun that passes through T so that it meets the incline from point B at point X to the right of the flagpole.

 

Triangle TBX has interior angles 73, 82 & 25 degrees, respectively. The shadow length BX is 20 meters long.

Use Law of Sines:

 

20/sin73 = TB/sin25 to get shadow length TB = 8.829 m.