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

Step-by-step 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, 

$\sin40^{\circ}=\frac{MN}{MO}\\\Rightarrow\ 0.6427=\frac{x}{50}\\\Rightarrow\ x=50\times0.6427\\\Rightarrow\ x=32.135$

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) = $\frac{Perpendicular}{Hypotenuse}$

⇒ sin (40°) =  $\frac{x}{50}$

⇒ x =  50 × sin (40°) 

⇒ x =  50 × 0.64
 
⇒ x =  32

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