SOLUTION: A vertical light pole on a hillside casts a shadow of 55 m long down the hill. If the angle of elevation of the sun is 48.3° and the angle of inclination of the hill is 21.4°. Fi

Algebra ->  Trigonometry-basics -> SOLUTION: A vertical light pole on a hillside casts a shadow of 55 m long down the hill. If the angle of elevation of the sun is 48.3° and the angle of inclination of the hill is 21.4°. Fi      Log On


   

Question 1181606: A vertical light pole on a hillside casts a shadow of 55 m long down the hill. If the angle of elevation of the sun is 48.3° and the angle of inclination of the hill is 21.4°. Find the height of the pole.
photo link- https://docs.google.com/document/d/1pcJWp55S6xj8Z-VsXH5Ci4gRmENIx-ER2J_MdSjuNHU/edit?usp=sharing
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Label the points on the diagram as follows:
A = downhill end of shadow
B = uphill end of shadow
C = top of pole

We have enough information to find all three angles of triangle ABC; we know the length of c (side AB) and we want to find the length of a (side BC). That combination of information (all three angles and one side) tells us to use the law of sines.

a%2Fsin%28A%29=c%2Fsin%28C%29

a+=+%28c%28sin%28A%29%29%29%2Fsin%28C%29

a+=+%2855%2Asin%2848.3-21.4%29%29%2Fsin%2890-48.3%29

Use a calculator....