Angle of depression

Question

From the top of a building the angle of depression of the top and the base of a flagpole is 20 degrees and 43 degrees respectively the flagpole is 12 meters away from the base of the building than the height of the flag pole is approximately 6.82 m

Answer 1

Hi Jules H.,

The top of the building to the top of the flagpole forms a right triangle with one angle being 20^o and an adjacent side of 12m. We can find the height (I will call this h_t) from the top of the flagpole to the top of the building (opposite side) using tan(θ) = opposite/adjacent. tan(20) = h_t/12m, or h_t = 12m*tan(20) = 4.367...m

The top of the building to the bottom of the flagpole forms a right triangle with one angle being 43^o and an adjacent side of 12m. We can find the height (I will call this h_b - this is the height of the building) from the top of the building to the bottom of the flagpole (opposite side) using tan(θ) = opposite/adjacent once again. tan(43) = h_t/12m, or h_b = 12m*tan(43) = 11.190...m

And the height of the flagpole is 11.190m - 4.367m ∼ 6.82m.

I hope this helps, Joe.