SOLUTION: 1. a rope 17 m long is attached to the top of a flagpole. The rope is just able to reach a point on the ground 8 m from the base of the pole. Find the height of the flagpole. 2

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 1. a rope 17 m long is attached to the top of a flagpole. The rope is just able to reach a point on the ground 8 m from the base of the pole. Find the height of the flagpole. 2      Log On

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Question 210462: 1. a rope 17 m long is attached to the top of a flagpole. The rope is just able to reach a point on the ground 8 m from the base of the pole. Find the height of the flagpole.
2.a vertical pole 3 m long casts a shadow 1 m long at the same time a building casts a shadow 12 m long. How tall is the building?
3.from the top of a 20 m lighthouse, the angle of depression of the nearest point on the beach is 8 degrees. Find the distance from the bottom of the lighthouse to the beach.
4. the diagonal of a square measures 9 radical 2 meters. Find the length of a side of the square.
Answer by Earlsdon(6294) About Me  (Show Source):
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1) Use the Pythagorean theorem:
c%5E2+=+a%5E2%2Bb%5E2 Substitute c = 17, a = 8, and b = the height of the flagpole.
17%5E2+=+8%5E2%2Bb%5E2 Solve for b.
+289+=+64%2Bb%5E2 Subtract 84 from both sides.
225+=+b%5E2 Take the square root of both sides.
15+=+b
The flagpole is 15 meters high.
2) Use the similar right triangles method: Let h = the building height.
3%2F1+=+h%2F12
h+=+12%2A3
h+=+36meters.
3) Use the tangent function: Let d = the distance from the base of the lighthouse to the point on the beach.
The tangent of the angle of depression (8 degs) is:
tan%288%29+=+20%2Fd
d+=+20%2Ftan%288%29
d+=+142.31 meters.
4) Let the side of the square = s, then, using the Pythagorean theorem:
%289sqrt%282%29%29%5E2+=+s%5E2%2Bs%5E2
81%2A%282%29+=+2s%5E2 Divide both sides by 2.
81+=+s%5E2 Take the square root of both sides.
s+=+9