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Right triangle word problem?
I'm supposed to use a right triangle to solve this problem:
At a point 200 feet from the base of the building, the angle of elevation to the bottom of a smokestack is 35 degrees, and the angle of elevation to the top is 53 degrees. Find the height of the smokestack alone. 8
Is it just me or is it awkwardly worded? The angles dont add up either.. 90 + 53 + 35 = 178
Help?
ignore the "8" at the end of the problem, typo
1 Answer
- 9 years agoFavorite Answer
No, it's not awkwardly worded at all.
Call the bottom of the building Point A. The point 200 ft away is Point B. The bottom of the smoke stack is Point C, and the top of the smokestack is Point D. Assuming that the building is NOT the Leaning Tower of Pisa, then angle CAB (and DAB) is a right angle. Hence, triangles ABC and ABD are both right triangles.
CD is the height of the smokestack. That's what you're looking for.
Given: Angle ABC is 35deg. Angle ABD is 53deg. ||AB|| = 200ft.
||CD|| = ||AD|| - ||AC||
||CD|| = ||AB||tan(<ABD) - ||AB||tan(<ABC)
||CD|| = 200tan(53) - 200tan(35)
||CD|| = 265.409 - 140.042
||CD|| = 125.367
The smokestack is approximately 125ft high.
