Trig question?

Question

A flagpole is perpendicular to the horizontal but is on a slope that rises 10 from the horizontal. The pole casts a 43-foot shadow down the slope and angle of elevation of the sun measured from the slope is 36 . How tall is the pole? Round your answer to the nearest 0.1 foot.

Thanks.

Answer 1

I assume you mean the slope rises 10 * degrees * from the horizontal.

Let
h = height flagpole

We have a triangle with three sides:

h = Flagpole
s = Shadow on the slope = 54 ft
z = From tip of slope to top of flagpole

H = angle between s and z = 36°
Z = angle between h and s
S = angle between h and z

Z = 90 + 10 = 100°

S = 180° - H - Z = 180° - 36° - 100° = 44°

Use the Law of Sines.

h/sinH = s/sinS

h = (sinH/sinS)s = [(sin 36°)/(sin 44°)] * 43 ≈ 36.4 ft

Answer 2

Let h be the height of the pole.
h/sin36 = 43/sin(90-36-10)
h = 36.4 ft