The height of tree is 32 meter
Solution:
Given that, The sun is at an angle of elevation of 58 degree
A tree casts a shadow 20 meters long on the ground
The sun, tree and shadow forms a right angled triangle
The figure is attached below
ABC is a right angled triangle
AC is the height of tree
AB is the length of shadow
AB = 20 meters
Angle of elevation, angle B = 58 degree
By definition of tan,
[tex]tan \theta = \frac{opposite}{adjacent}[/tex]
In this right angled triangle ABC,
opposite = AC and adjacent = AB
Therefore,
[tex]tan\ 58 = \frac{AC}{AB}\\\\tan\ 58 = \frac{AC}{20}\\\\1.6 = \frac{AC}{20}\\\\AC = 1.6 \times 20\\\\AC = 32[/tex]
Thus height of tree is 32 meter
