Question

A balloon is connected to a meteorological ground station by a cable of length, 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.
[Consider $\sqrt{3}=1.73$]

• A.
  150 m
• B.
  185.975 m
• C.
  145.8 m
• D.
  137.6 m

Answer 1

The correct option is B

185.975 m
Let the height of the balloon from the ground = $h$ m
Given, the length of the cable = $215$ m and the inclination of the cable is ${60}^{\circ }$ .


In ΔABC,

$sin{60}^{\circ }=\frac{AB}{AC}$

$\frac{\surd 3}{2}=\frac{h}{215}$

$h=\frac{215\surd 3}{2}$

$h=\frac{215\times 1.73}{2}$

$h=185.975m$

Hence, the height of the balloon from the ground is approximately 185.975 m.