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

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(6103) (Show Source):
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1) Use the Pythagorean theorem:
Substitute c = 17, a = 8, and b = the height of the flagpole.
Solve for b.
Subtract 84 from both sides.
Take the square root of both sides.

The flagpole is 15 meters high.
2) Use the similar right triangles method: Let h = the building height.

meters.
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:

meters.
4) Let the side of the square = s, then, using the Pythagorean theorem:

Divide both sides by 2.
Take the square root of both sides.