Question

solving for side lengths of ri
instruction
ng the length of a shadow
ater tower is 52 meters tall and the straight-line dist
end of the shadow it creates is at a 40° angle with
th of the tower’s shadow, rounded to the nearest
. $\tan(b)=\frac{opposite}{adjacent}$
. the opposite side is 52 m.
. the adjacent side is $x$.
$\tan(40^circ)=\frac{62}{x}$

Explanation:

Step1: Identify the formula and values

We use the tangent function formula $\tan(B) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $B = 40^\circ$, opposite side (height of tower) is $52$ meters, and adjacent side is $x$ (length of shadow). So the equation is $\tan(40^\circ) = \frac{52}{x}$.

Step2: Solve for \( x \)

Rearrange the equation to solve for \( x \):

$$ x = \frac{52}{\tan(40^\circ)} $$

We know that $\tan(40^\circ) \approx 0.8391$. Substitute this value into the equation:

$$ x = \frac{52}{0.8391} \approx 61.97 $$

Rounding to the nearest whole number, $x \approx 62$.

Answer:

The length of the tower’s shadow is approximately 62 meters.