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 rock's shadow should end when it's 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°. 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.

Answer 1

Answer:

Archimedes went to sleep 7.51 meters from the rock.

Step-by-step explanation:

We are told that the sunlight reaches the ground at an angle of 43°,  and that the rock is 7 meters tall.

The distance $d$ from the rock where Archimedes should sleep is:

$tan (43)=\frac{7}{d}$

$d=\frac{7}{tan(43)} =\boxed{7.51\:meters}$