Can anyone figure this out... I'm just so bad at math problems.?
2016-11-06 7:44 pm
A lighthouse sits at the edge of a cliff. A ship at sea level is 1100 meters from the base of the cliff. The angle of elevation from sea level to the base of the lighthouse is 48.1 degrees. The angle of elevation from sea level to the top of the lighthouse is 50.5 degrees. Find the height of the lighthouse from the top of the cliff.
回答 (2)
2016-11-06 8:00 pm
✔ 最佳答案
height of cliff = 1,100tan(48.1°) ≅ 1,225.97 mtop of lighthouse to sea level = 1,100tan(50.5°) ≅ 1,334.41 m
height of lighthouse = 1,334.41 - 1,225.97 ≅ 108.44 m
2016-11-06 7:48 pm
First figure out the height of the cliff (base of lighthouse) above sea level.
h1 = 1100 tan(48.1°)
Then figure out the height of the lighthouse top above sea level.
h2 = 1100 tan(50.5°)
Then subtract to get the height of the lighthouse.
1100(tan(50.5°) - tan(48.1°))
≈ 108 meters
Note: In both cases, you have the angle of elevation, the adjacent leg (distance to base of cliff) and the opposite leg (cliff or cliff+lighthouse).
Using the SOH-CAH-TOA mnemonic, you want to use TOA because you have Opposite and Adjacent involved. Hence the trig function involved is Tangent.
Use:
tan(angle) = opposite/adjacent
Example:
tan(48.1°) = h1 / 1100
--> h1 = 1100 tan(48.1°)
h1 = 1100 tan(48.1°)
Then figure out the height of the lighthouse top above sea level.
h2 = 1100 tan(50.5°)
Then subtract to get the height of the lighthouse.
1100(tan(50.5°) - tan(48.1°))
≈ 108 meters
Note: In both cases, you have the angle of elevation, the adjacent leg (distance to base of cliff) and the opposite leg (cliff or cliff+lighthouse).
Using the SOH-CAH-TOA mnemonic, you want to use TOA because you have Opposite and Adjacent involved. Hence the trig function involved is Tangent.
Use:
tan(angle) = opposite/adjacent
Example:
tan(48.1°) = h1 / 1100
--> h1 = 1100 tan(48.1°)
收錄日期: 2021-04-21 23:54:49
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20161106114442AAMM6mW