Question

A 50-foot support cable is attached to a vertical pole at a point that is 5 feet from the top of the pole. The cable stretches diagonally to the ground and forms a 40° angle with the ground. What is the total height, h, of the vertical pole?

Answer 1

Answer: The total height of the vertical pole from ground is 37.135 ft

Explanation:

Given : Length of support cable = 50 feet

Let x be the height of point where cable is attached from the ground.

We know that
`\sin\theta=\frac{\text{side opposite to }\theta}{\text{hypotenuse}}`

From the figure,

`\sin40^(\circ)=(MN)/(MO)\\\Rightarrow\ 0.6427=(x)/(50)\\\Rightarrow\ x=50*0.6427\\\Rightarrow\ x=32.135`

The total height of the pole = x+5= 32.135+5= 37.135 feet

Therefore, total height of pole is = 37.135 ft

Answer 2

The total height of the vertical pole from ground is 37 ft

From the figure,

sin (Ф) =
`(Perpendicular)/(Hypotenuse)`

⇒ sin (40°) =
`(x)/(50)`

⇒ x = 50 × sin (40°)

⇒ x = 50 × 0.64

⇒ x = 32

Therefore, total height of pole is 32 + 5 = 37 ft