Question

finding the length of a shadow
a water tower is 52 meters tall and the straight - line distance from the top of the tower to the end of the shadow it creates is at a 40° angle with the ground. what is the approximate length of the tower’s shadow, rounded to the nearest whole number?

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the height of the tower is the opposite side and the length of the shadow is the adjacent side with respect to the given angle. We use the tangent function: $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 40^{\circ}$ and the opposite side (height of the tower) $h = 52$ meters, and we want to find the adjacent side $x$ (length of the shadow). So, $\tan40^{\circ}=\frac{52}{x}$.

Step2: Solve for $x$

We can re - arrange the equation $\tan40^{\circ}=\frac{52}{x}$ to $x=\frac{52}{\tan40^{\circ}}$. Since $\tan40^{\circ}\approx0.8391$, then $x=\frac{52}{0.8391}\approx62$.

Answer:

62