Question

. A hot air balloon hovers 100 feet about the ground. The balloon is tethered to the ground with arope that is 250 feet long. At what angle of elevation, is the rope attached to the ground? Roundyou answer to the nearest degree.250 feet100 feet

Answer 1

hello

to solve this question, we need to sketch this situation to give us a better illustration

to find the angle of elevation, we can use trigonometric ratios here

SOHCAHTOA

`\begin{gathered} \text{SOH}=\sin \theta=\frac{\text{opp}}{\text{hyp}} \\ \text{CAH}=\cos \theta=(adj)/(hyp) \\ \text{TOA}=\tan \theta=\frac{\text{opp}}{\text{adj}} \end{gathered}`

since we have the value of hypothenus and opposite, we can use the sine angle to find the angle of elevation

`\begin{gathered} \sin \theta=(opp)/(hyp) \\ \text{opp}=100 \\ \text{hyp}=250 \\ \sin \theta=(100)/(250) \\ \sin \theta=0.4 \\ \text{take the sine inverse of 0.4} \\ \theta=\sin ^(-1)0.4_{} \\ \theta=23.578^0 \\ \theta\approx24^0 \end{gathered}`

from the calculation above, the angle of elevation is equal to 24 degrees