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?

Answer 1

It's 7.51

Explanation:

Answer 2

The rock is 924 meters far from the place where Archimedes went to sleep

Explanation:

Right Triangles

They are special triangles where one of its internal angles is 90°. The basic trigonometric ratios for the sine, cosine, and tangent are:

`\displaystyle sin\theta=(y)/(h)`

`\displaystyle cos\theta=(x)/(h)`

`\displaystyle tan\theta=(y)/(x)`

Where h is the hypotenuse of the triangle, y and x are the opposite and adjacent legs to the angle
`\theta` respectively.

The rock that Archimedes used to wake him up is 555 meters tall. The height of the rock is opposite to the horizontal angle of 31°. That is enough information to find the horizontal distance to the rock (x). We need to use the tangent ratio:

`\displaystyle tan31^o=(555)/(x)`

Solving for x

`\displaystyle x=(555)/(tan31^o)=924\ m`

The rock is 924 meters far from the place where Archimedes went to sleep