7. the sun is at an angle of elevation of 58º. a tree casts a shadow 20 meters long on
the ground. how tall is the tree?

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,

In this right angled triangle ABC,

opposite = AC and adjacent = AB

Therefore,

Thus height of tree is 32 meter

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