Question

Find the angle of elevation of the sun from the ground when a tree that is 14ft tall casts a shadow 16ft long. Round to the nearest degrees

Answer 1

Question:

Find the angle of elevation of the sun from the ground when a tree that is 14ft tall casts a shadow 16ft long. Round to the nearest degrees.

Solution:

Consider the following diagram of the problem:

Applying the appropriate trigonometric identity to the right triangle in the diagram, we obtain:

$\tan (\theta)=\text{ }\frac{14}{16}$

now, applying to both sides of the equation the inverse function of the tangent, we get:

$\tan ^{-1}(\tan (\theta))=\text{ }\tan ^{-1}(\frac{14}{16})$

this is equivalent to:

$\theta=tan^{-1}(\frac{14}{16})=\text{ 41.185}\approx41.19$

then, the correct answer is:

$\theta=41.19$