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:
[tex]\tan \alpha = \frac{h}{w}[/tex]
Where:
[tex]\alpha[/tex] - Elevation angle, measured in sexagesimal degrees.
[tex]h[/tex] - Height of the tree, measured in meters.
[tex]w[/tex] - Length of the tree shadow, measured in meters.
The height of the tree is cleared in the equation:
[tex]h = w\cdot \tan \alpha[/tex]
If [tex]w = 51\,m[/tex] and [tex]\alpha = 24^{\circ}[/tex], the height is:
[tex]h = (51\,m)\cdot \tan 24^{\circ}[/tex]
[tex]h \approx 22.707\m[/tex]
The tree is approximately 22.707 meters tall.
