Question

A balloon is connected to an electric pole by a cable of length 215 metre incline at an angle 60 degree to the horizontal. Determine the height of the balloon from the ground. Also, find the height of the balloon if the angle of inclination is changed from 60 degree to 30 degree.

Answer 1

Answer:

The height of the balloon for 60 degree inclination will be 186.2 m

The height of the balloon for 30 degree inclination will be 107.5 m

Step-by-step explanation:

Let the height of the balloon is p

length of the pole = 215 m

This forms a right angled triangle, so

sin 60 = p/h

=> 0.866 = p/215

=> p = 0.866 x 215 = 186.2 m

Hence the height of the balloon from the ground is 186.2 m

If the angle of inclination becomes 30 degree, then

sin 30 = p/h

=> 0.5 = p/215

=> p = 0.5 x 215 = 107.5 m

Hence the height of the balloon from the ground for 30 degree inclination will be 107.5 m

Answer 2

Answer:

Height of the baloon from the ground when the angle of elevation 60 degrees is 187.19 meters.

Height of the baloon from the ground when the angle of elevation 30 degrees is 107.5 meters.

Step-by-step explanation:

Let A be the postion of the baloon when the angle of elevation is 60 degrees.

Let A' be the postion of the baloon when the angle of elevation is 30 degrees.

In triangle ABC,

$sin60=\frac{AB}{AC}\\\\\frac{\sqrt{3}}{2}=\frac{AB}{215}\\\\AB=215*\frac{\sqrt{3}}{2}\\\\AB=215*\frac{1.732}{2}\\\\AB=215*(0.866)\\\\AB=186.19\:meters$

In triangle A'BC,

$sin30=\frac{AB}{AC} \\\\\frac{1}{2}=\frac{A'B}{215} \\\\A'B=215*\frac{1}{2} \\\\A'B=107.5\:meters$