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 8AM, 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:

7.51 m

Step-by-step explanation:

d = 7 × tan43° = 7 ÷ 0.932515086.. = 7.50658097.......

d ≈ 7.51 m  

Answer 2

Answer:

7.50 m

Step-by-step explanation:

Sunlight, rock and its shade form a right triangle

Triangle has 43∘ opposite to rock which is 7 m tall

x- is the shade of the rock or base of the triangle

• 7/x= tan 43∘
• x=7/tan 43∘= 7/0.933= 7.50 m

Answer: 7.50 m