Question

archimedes went to sleep beside a big rock. he wanted to get up at 8 am, but the alarm clock was yet to be invented! he decided to sleep at the spot where the rocks shadow should end when its 8 am so as to be awakened by the direct sunlight.

archimedes knew that at 8 am, the sunlight reaches the ground at an angle of $43^{\circ}$. the rock beside which he slept was 7 meters tall.

how far from the rock did archimedes go to sleep?
round your final answer to the nearest hundredth.
______ meters

Explanation:

Step1: Define trigonometric relation

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 43^\circ$, opposite side = 7 m (rock height), adjacent side = distance $x$ we need to find.

Step2: Rearrange to solve for $x$

$x = \frac{7}{\tan(43^\circ)}$

Step3: Calculate the value

First, find $\tan(43^\circ) \approx 0.9325$, then $x \approx \frac{7}{0.9325} \approx 7.51$

Answer:

7.51 meters