Question

What is the angle of elevation of the sun when a 44 ft mast casts a 13ft shadow?

Answer 1

here

Explanation:

Let the angle of elevation be \thetaθ

\begin{gathered} \therefore \tan \: \theta = \frac{height \: of \: mast}{height \: of \: shadow} \\ \\ \therefore \tan \: \theta = \frac{44}{14} \\ \\ \therefore \tan \: \theta = 3.14285714 \\ \\ \therefore \: \theta = {\tan}^{ - 1} (3.14285714) \\ \therefore \: \theta = 72.349875765 \degree \\ \\ \huge \red{ \boxed{\therefore \:\theta = 72.35 \degree}}\end{gathered}

∴tanθ=

heightofshadow

heightofmast

∴tanθ=

14

44

∴tanθ=3.14285714

∴θ=tan

−1

(3.14285714)

∴θ=72.349875765°

∴θ=72.35°

Hence, angle of elevation of the sun is 72.35°.