Question

(from unit 6)

1. (technology required.) the sun is 62 degrees above the horizon. a tree casts a shadow that is 12 feet long. how tall is the tree?

Explanation:

Step1: Define variables and trigonometric relation

Let $h$ = height of the tree. The sun's angle above the horizon forms a right triangle where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\text{shadow length}}$.

Step2: Substitute known values

$\theta = 62^\circ$, shadow length = 12 ft. Rearrange to solve for $h$:
$h = 12 \times \tan(62^\circ)$

Step3: Calculate the value

Use $\tan(62^\circ) \approx 1.8807$
$h \approx 12 \times 1.8807$

Answer:

The tree is approximately 22.57 feet tall.