A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 18° with the horizontal. The flagpole casts a 14-meter shadow up the slope when the angle of elevation from the tip of the shadow to the sun is 21°.

Question

(b) Write an equation involving the unknown quantity h.

(c) Find the height of the flagpole. (Round your answer to two decimal places.)
h = m

Answer 1

define
point A is flagpole base
Point B is flagpole top
point C is where shadow ends up slope

<ABC = 90-21 = 69
<BAC = 90-18 = 72
so
<BCA = 180 - 69 - 72 = 39

now law of sines
sin 69 / 14 = sin 39 / h