Question

malik is playing with his cat using a laser pointer. he stands to the left of a table pointing the laser downward at an angle. the laser hits a mirrored centerpiece on the table, reflecting off of the mirror onto the wall on the right of the table. the height of the laser pointer from the table top is 91 cm. the mirrored centerpiece is 119 cm from the left end of the table and 79 cm from the right end of the table.
the laser reflected off of the mirror at the same angle, relative to the table, that it reached the mirror.
figure: two right triangles with a common vertex at the mirror. left triangle: vertical leg 91 cm (malik to table), horizontal leg 119 cm (malik to mirror). right triangle: vertical leg ? cm (wall to table), horizontal leg 79 cm (mirror to wall). figure not to scale.
how high off of the table, in centimeters, did the laser hit the wall? round to the nearest unit.
blank cm
image of a laser pointer with a green laser beam, legal and compliant

Explanation:

Step1: Identify Similar Triangles

The two right triangles (from Maliq to mirror and mirror to wall) are similar because the angle of incidence equals the angle of reflection, so their corresponding angles are equal.

Step2: Set Up Proportion

Let \( h \) be the height on the wall. The ratio of height to base should be equal for both triangles. So, \(\frac{91}{119}=\frac{h}{79}\).

Step3: Solve for \( h \)

Cross - multiply: \( 119h = 91\times79 \). Calculate \( 91\times79 = 7189 \). Then \( h=\frac{7189}{119}\approx60.41\approx60 \).

Answer:

60