Question

Scientists bounce a laser beam off a mirror. It reflects at the same angle as it hits the

mirror and is detected by an instrument several inches away.
Calculate the total distance of the laser beam travels. Round to the nearest tenth if necessary.

Answer 1

Answer and Step-by-step explanation:

Simply use triangles to find the length of the lasers.

The first triangle consists of the sides of 12 inches, 18 inches, and the laser (which is the hypotenuse).

Use the Pythagorean theorem to solve for the hypotenuse.

(
`a^(2)+ b^(2) = c^(2)`)

`12^(2) +18^(2) = l^(2) \\\\144 + 324 = l^(2) \\\\468 = l^(2) \\\\Square-root-both-sides\\\\\ \\√(468) = l`

l ≈21.633

Now, we solve the other triangle.

`9^(2) +6^(2) = l^(2) \\\\81 + 36 = l^(2) \\\\117 = l^(2) \\\\Square-root-both-sides\\\\√(117) =l\\l = 10.8167`

Now, add those two hypotenuses.

21.6333 + 10.8167 = 32.45

32.45 rounds up to 32.5

32.5 is the total distance the laser beam travels.

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