Question

from a hot - air balloon, lillian measures a $38^{circ}$ angle of depression to a landmark thats 704 feet away, measuring horizontally. whats the balloons vertical distance above the ground? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the horizontal distance is 704 feet (adjacent side to the angle of depression), and the vertical distance \( x \) is the opposite side to the angle of depression (which is equal to the angle of elevation from the landmark to the balloon, \( 38^\circ \)). So we use the tangent function: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \)

Step2: Substitute the values

\( \tan(38^\circ)=\frac{x}{704} \)

Step3: Solve for \( x \)

Multiply both sides by 704: \( x = 704\times\tan(38^\circ) \)
Calculate \( \tan(38^\circ)\approx0.7813 \)
Then \( x = 704\times0.7813\approx549.0 \)

Answer:

549.0