Question

A 30 feet tall building casts a 5 foot shadow. what is the suns angle of inclination

Answer 1

Make a drawing of the situation:

Recalling the tangent trigonometric relationship, if the angle of inclination is A, then:

$\begin{gathered} \tan (A)=\frac{30\text{ feet}}{5\text{ feet}} \\ \Rightarrow\tan (A)=6 \end{gathered}$

Use the inverse tangent function to find the value of A:

$A=\tan ^{-1}(6)$

Use a calculator to find the numerical value of the inverse tangent of 6:

$A=80.52767779\ldots$

Therefore, the angle of inclination of the Sun is approximately 80.5°.