Answer:
The rock is 924 meters far from the place where Archimedes went to sleep
Step-by-step 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:
[tex]\displaystyle sin\theta=\frac{y}{h}[/tex]
[tex]\displaystyle cos\theta=\frac{x}{h}[/tex]
[tex]\displaystyle tan\theta=\frac{y}{x}[/tex]
Where h is the hypotenuse of the triangle, y and x are the opposite and adjacent legs to the angle [tex]\theta[/tex] 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:
[tex]\displaystyle tan31^o=\frac{555}{x}[/tex]
Solving for x
[tex]\displaystyle x=\frac{555}{tan31^o}=924\ m[/tex]
The rock is 924 meters far from the place where Archimedes went to sleep
