Question

A tree casts a 12 foot shadow while the sun is at an angle of elevation of 58º. Use

Answer 1

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,

$tan \theta = \frac{opposite}{adjacent}$

In this right angled triangle ABC,

opposite = AC and adjacent = AB

Therefore,

$tan\ 58 = \frac{AC}{AB}\\\\tan\ 58 = \frac{AC}{20}\\\\1.6 = \frac{AC}{20}\\\\AC = 1.6 \times 20\\\\AC = 32$

Thus height of tree is 32 meter