Question

question
if a tree has a height of 68 feet, what would be the angle of elevation from level ground measured from 78 feet away? round your answer to the nearest tenth of a degree.
answer attempt 1 out of 4

Explanation:

Step1: Define trigonometric relation

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, opposite side = tree height = 68 ft, adjacent side = distance from tree = 78 ft.
$\tan(\theta) = \frac{68}{78}$

Step2: Simplify the fraction

Reduce the fraction to simplify calculation.
$\tan(\theta) = \frac{34}{39} \approx 0.8718$

Step3: Solve for $\theta$

Use inverse tangent to find the angle.
$\theta = \arctan(0.8718)$

Step4: Calculate and round

Compute the value and round to nearest tenth.
$\theta \approx 41.0^\circ$

Answer:

$41.0^\circ$