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 3 out of 4

Explanation:

Step1: Define trigonometric ratio

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

Step2: Simplify the ratio

Reduce the fraction and calculate its decimal value.
$\tan(\theta) \approx 0.8718$

Step3: Solve for $\theta$

Use the inverse tangent function to find the angle.
$\theta = \tan^{-1}(0.8718)$

Step4: Calculate and round

Compute the angle and round to the nearest tenth.
$\theta \approx 41.1^\circ$

Answer:

$41.1$