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.

7.5065 m.

Step-by-step explanation:

Let, he has to sleep at d distance from the rock.

Then, tan43 = 7 / d

=> d = 7 / tan43

=> d = 7.5065 (Approx.)

[If there's any mistake, please inform me]

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180

justin bieber ml.