Question

Charlie is late for the hot-air balloon rally. He stops his car 65 meters from a hot-air balloon already in flight. While Charlie watches the balloon ascend, he tilts his eyes up from 28º until he is watching at an angle of elevation of 66º. Find the vertical distance to the nearest tenth of a meter that the balloon ascended while Charlie watched.

Answer 1

Answer: 111.4m

Explanation:

1) Trigonometric ratios

You only need to use tangent ratio.

tangent ratio = opposite-leg / adjacent-leg = balloon height / horizontal distance

2) First, find the height of the ballon when he is watching at an angle of elevation of 28°

tangent ratio = opposite-leg / adjacent-leg = balloon height / horizontal distance

tan(28°) = balloon height/65m ⇒balloon height = tan(28°)×65m

balloon height = 34.56m

3) Second, find the height of the balloon,when he is watching at an angle of elevation of 66°

tan(66°) = height of the balloon / 65m ⇒ height of the balloon = tan(66°)×65m

height of the balloon = 145.99m

4) Vertical distance the balloon ascended while Charlie watched.

Subtract the final initial height from the final height:

145.99m - 34.56m = 111.43m

4) Round to the nearest tenth: 111.4 m