Question

Archimedes went to sleep beside a big rock. He wanted to get up at 777 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 777 AM so as to be awakened by the direct sunlight.
Archimedes knew that at 777 AM, the sunlight reaches the ground at an angle of 31^\circ31
∘
31, degrees. The rock beside which he slept was 555 meters tall.
How far from the rock did Archimedes go to sleep?
Round to the nearest hundreth.

Answer 1

Answer:

8.3 meters I am going to assume that Archimedes is capable of determining the horizontal distance from the peak of the rock to the ground. So we have a right triangle, with and angle of 31 degrees and the opposite side being 5 meters tall. So we want the adjacent side (the horizontal distance). This screams "tangent" which is defined as opposite over adjacent. So 5/x = tan(31) 5 = x*tan(31) 5/tan(31) = x 5/0.600860619 = x 8.321397412 = x So Archimedes needs to place his head 8.3 meters away from the point directly underneath the peak of the rock. Too bad for him that not only hasn't the alarm clock been invented, but meter itself won't be developed for about another 2000 years either.

Step-by-step explanation: