A vertical pole is supported by two ropes staked to the ground on opposite sides of the pole. One rope is 8 meters long, and the other is 7 meters. The distance between the stakes is 6 meters, and the height of the pole is meters. a3.30
b3.78
c6.17
d6.78
2 answers:
Establish two right triangles, both with the height of the pole, h. Call x the distance from the pole to one stake. Then the distance from the other stake to the pole is 6 -x. Apply Pytagora's equation to both triangles. 1) h^2 = 7^2 - x^2 2) h^2 = 8^2 - (6-x)^2 Eaual 1 to 2 7^2 - x^2 = 8^2 - 6^2 +12x -x^2 12x = 7^2 -8^2 +6^2 = 49 -64 + 36 = 21 x = 1.75 Substitue x-value in 1 h^2 = 49 - (1.75)^2 = 45.94 h = sqrt(45.94) = 6.78 Answer: option d.
The correct answer is d. 6.78 Here's how to solve this problem in order to get the height of the pole. Let x = the distance of the 7-m pole to the vertical pole. Let 6-x = the distance of the 8-m pole to the vertical pole. X^2 + h^2 = 7^2 <span>(6-X)^2 + h^2 = 8^2 x^2 + h^2 = 49 (6-x) + h^2 = 64 ---------------------- x^2 - (6-x)^2 = 15 x^2 - (36 - 12x + x^2) = 15 x^2 - 36 + 12x - x^2 = 15 x = 7/4 </span><span>X^2 + h^2 = 7^2 </span>(7/4)^2 + h^2 = 49 h^2 = 49 - 3.0625 h = sqrt (45.9375) h = 6.78
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