Question

Archimedes went to sleep beside a big rock. He wanted to get up at 888 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 888 AM so as to be awakened by the direct sunlight. Archimedes knew that at 888 AM, the sunlight reaches the ground at an angle of 43^\circ43 ∘ 43, degrees. The rock beside which he slept was 777 meters tall. How far from the rock did Archimedes go to sleep?

Answer 1

Step-by-step explanation:

Given 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, degrees. The rock beside which he slept was 7 meters tall. How far from the rock did Archimedes go to sleep?

• Archimedes wanted  to sleep beside the rock and wanted to wake up at 8 am and needed an alarm. But an alarm was not invented at that time and so he chose to wake up as to where the sunlight reaches him as soon as the day begin. The rock which Archimedes slept was 7 m tall. The sunlight reached the ground at an angle of 43 degree.
• So the shadow will be the hypotenuse and the rock will be the opposite side which is 7 m tall.So a right angled triangle will be formed.
• Let the adjacent side be a
• Now tan theta = opposite side / adjacent side
• Or tan 43 = 7 / a
• Or a . tan 43 = 7
• Or a = 7 / tan 43
•         = 7 / 0.9325
• Or a = 7.506 m

Answer 2

7.5 meter from the rock did Archimedes go to sleep.

Given:

Archimedes went to sleep beside a big rock.

He wanted to get up at 8 AM.

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.

To find:

How far from the rock did Archimedes go to sleep.

Explanation:

Refer the below figure.

Consider length of rock wall is = BC =  7 meters

Sunlight reaches the ground at an angle of 43° from back of the wall

Hence ∠ABC = 43°

From given figure,

tan($\theta$) = $\frac{BC}{AC}$

tan( 43 ) =  $\frac{7}{AC}$

AC =7.5 meter.

So that 7.5 meter from the rock did Archimedes go to sleep.

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