Question

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

Answer 1

Answer:

The tree is approximately 22.707 meters tall.

Step-by-step explanation:

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

$\tan \alpha = \frac{h}{w}$

Where:

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

$h$ - Height of the tree, measured in meters.

$w$ - 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.