The sun is 24 degreesabove the horizon. It makes a 51 m long shadow of a tall tree. how talll is the tree

Question

asked Oct 15, 2021 15.3k views

1 Answer

Jankyz · Answer 1 · 2021-10-21T02:35:03+0000

Answer:

The tree is approximately 22.707 meters tall.

Explanation:

The geometric diagram of the problem is included below as attachment. The height of the tree is found by means of trigonometric functions:

$\tan \alpha = (h)/(w)$

Where:

$\alpha$ - Elevation angle, measured in sexagesimal degrees.

- Height of the tree, measured in meters.

- Length of the tree shadow, measured in meters.

The height of the tree is cleared in the equation:

$h = w\cdot \tan \alpha$

If
$w = 51\,m$ and
$\alpha = 24^(\circ)$ , the height is:

$h = (51\,m)\cdot \tan 24^(\circ)$

$h \approx 22.707\m$

The tree is approximately 22.707 meters tall.