- #1

RayDonaldPratt

- 9

- 9

- Homework Statement
- "A woman standing on a hill sees a building that she knows is 55 feet tall. The angle of depression to the bottom of the building is 27°, and the angle of elevation to the top of the building is 35°. Find the straight line distance from the woman to the building."

- Relevant Equations
- ((35/62)*55)/Adj. = Tan 35°; so, Adj.= ((35/62)*55)/Tan 35°, and so Adj. = ≈44.34169214.

Similarly:

((27/62)*55)/Adj. = Tan 27°; so, Adj.= ((27/62)*55)/Tan 27°, and so Adj. = ≈47.00768711.

It's the same adjacent side, so why are the computed lengths so different?

I'm doing self-study out of a free .PDF book entitled, Trigonometry, by Richard W. Beveridge (©June 18, 2014).

The problem I'm interested in is as follows:

"A woman standing on a hill sees a building that she knows is 55 feet tall. The angle of depression to the bottom of the building is 27°, and the angle of elevation to the top of the building is 35°. Find the straight line distance from the woman to the building."

I drew a diagram and placed my stick figure woman standing above the ground at an unknown height, but roughly lower than half of the building, and I drew a line from her eyes to the top of the building (≈35°), another line straight from her eyes perpendicular to the building, and then the final line from her eyes to the bottom of the building (≈27°). My task was to find the distance of the line straight from her eyes perpendicular to the building.

My first conundrum was how to correctly divide the 55' building into two parts so that I could get the lengths of the opposite sides of the two triangles formed by the lines from her eyes to the side of the building. I figured out that her entire field of view is 35° + 27° = 62° and that the measure of the upper half of the building would be 35/62 of 55' and that the lower half would be 27/62 of 55'.

From there, I could use my calculator's trigonometry features to find the distance of the line perpendicular to the building from her eyes using either triangle since both triangles have the same adjacent side from her eyes. However, I got thrown for a loop: the same side for either triangle computed out to seriously different lengths: ≈44.34' for the 35° triangle, and ≈47.01' for the 27° triangle. Worse, the book gives the answer of ≈45.5'. The only way that I get close to that answer is if I add both of my full answers together and then divide by two: (44.34169214 + 47.00768711) / 2 = 45.67468962.

If trigonometry is that bad, and I did this correctly, then I am okay with that; but, if I did something wrong, I would like to know what it is. Please.

The problem I'm interested in is as follows:

"A woman standing on a hill sees a building that she knows is 55 feet tall. The angle of depression to the bottom of the building is 27°, and the angle of elevation to the top of the building is 35°. Find the straight line distance from the woman to the building."

I drew a diagram and placed my stick figure woman standing above the ground at an unknown height, but roughly lower than half of the building, and I drew a line from her eyes to the top of the building (≈35°), another line straight from her eyes perpendicular to the building, and then the final line from her eyes to the bottom of the building (≈27°). My task was to find the distance of the line straight from her eyes perpendicular to the building.

My first conundrum was how to correctly divide the 55' building into two parts so that I could get the lengths of the opposite sides of the two triangles formed by the lines from her eyes to the side of the building. I figured out that her entire field of view is 35° + 27° = 62° and that the measure of the upper half of the building would be 35/62 of 55' and that the lower half would be 27/62 of 55'.

From there, I could use my calculator's trigonometry features to find the distance of the line perpendicular to the building from her eyes using either triangle since both triangles have the same adjacent side from her eyes. However, I got thrown for a loop: the same side for either triangle computed out to seriously different lengths: ≈44.34' for the 35° triangle, and ≈47.01' for the 27° triangle. Worse, the book gives the answer of ≈45.5'. The only way that I get close to that answer is if I add both of my full answers together and then divide by two: (44.34169214 + 47.00768711) / 2 = 45.67468962.

If trigonometry is that bad, and I did this correctly, then I am okay with that; but, if I did something wrong, I would like to know what it is. Please.