Question

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

Answer 1

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.

Answer 2

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 
(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


X^2 + h^2 = 7^2 
(7/4)^2 + h^2 = 49
h^2 = 49 - 3.0625
h = sqrt (45.9375)
h = 6.78