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Before climbing, carlos wants to know the height of the rock wall he will climb. He places a mirror on the ground between him and the base of the wall, so he can see rhe top of the wall in the mirror. The mirror is 4 ft from carlos and 36 ft from the base of the wall. Carlos is 5.8 fr tall

Respuesta :

elcharly64

Answer:

The rock is 52.2 feet high

Step-by-step explanation:

Similar Triangles

The triangle formed by the rock, mirror and the ground is similar to the triangle formed by Carlos, the mirror and the ground (see image below). This means its sides are proportional, and

[tex]\displaystyle \frac{H}{h}=\frac{X}{x}[/tex]

We want to calculate the height of the rock, thus we solve for H

[tex]\displaystyle H=\frac{h.X}{x}[/tex]

[tex]\displaystyle H=\frac{5.8\times 36}{4}=52.2 feet[/tex]

[tex]\boxed{\text{The rock is 52.2 feet high}}[/tex]

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