Question

When the sun is at a certain angle in the sky, a 50-foot building will cast a -foot shadow. What is the length of the shadow in feet cast by a 20 -foot pole at the same time? Enter only the number.

Answer 1

Answer:

0.40 foot

Step-by-step explanation:

In the first case, a 50 - foot building casts a- foot shadow (1-foot). Let the angle of elevation of the sun from the shadow be represented by θ.

Then:

Tan θ = $\frac{opposite}{adjacent}$

Tan θ = $\frac{50}{1}$

Tan θ = 50

⇒ θ = $Tan^{-1}$ 50

      = 88.8542

      = $88.85^{o}$

The angle of elevation is approximately $88.85^{o}$.

For a 20-foot pole,

Tan θ = $\frac{opposite}{adjacent}$

Tan $88.85^{o}$ = $\frac{20}{x}$

x = $\frac{20}{Tan 88.85^{o} }$

 = 0.4015

 = 0.40 foot

The length of the shadow of the pole is 0.40 foot.