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

Draw one horizontal (ground), one vertical (pole). From the base of the pole draw the 20 m shadow line at 8 ° with the horizontal to the left (supposing the sun rays are coming from the right). Draw a sun ray from the top of the pole to the horizontal passing by the end of the shadow. We have two triangles; in the rectangle one angle is 17° and the top angle is 90-17= 73°. Now in the smaller triangle, the angle at the base of the pole is 90-8= 82° and the angle at the end of the shadow is 180-73-82=25° Apply the law of sines and is done.

Answer 2

I drew a figure representing this situation.  Place a vertical segment TB on the horizon; points T & B are the top and botom endpoints of the flagpole.  The Sun can be placed to the left & above TB such that the angle of elevation to Sun from T is 17^o. Extend the Sun's ray passing through T downward & to the right such that it intersects, at X, the inclined hill.

 

Triangle TBX has interior angles measuring 73, 82 and 25 degrees, respectively.

 

The shadow,BX, is 20 m. Use the Law of Sines:  20/sin73 = TB/sin25 to get TB = 8.839 meters.