Question

For a project in his Geometry class, Montraie uses a mirror on the ground to measure the height of his school’s football goal post. He walks a distance of 13.15 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. He then walks 6.25 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the goalpost clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.35 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

Answer 1

0.91 meter

Explanation:

We can use similar triangles to solve this problem. Let h be the height of the goalpost, and let x be the distance from the mirror to the base of the goalpost. Then, we have:h/x = (h + 1.35)/(x + 13.15 + 6.25)Simplifying this equation, we get:h(x + 19.4) = x(h + 1.35)Expanding and rearranging, we get:hx + 19.4h = hx + 1.35xSolving for h, we get:h = 1.35x/19.4We can now substitute the given values to find the height of the goalpost:x = 13.15 meters

h = 1.35(13.15)/19.4 = 0.9105 metersTherefore, the height of the goalpost is approximately 0.91 meters (rounded to the nearest hundredth).

Answer 2

Explanation:

Let's call the height of the goalpost "h". We want to find the value of "h".

From Montraie's perspective, he sees the top of the goalpost and its reflection in the mirror. The distance from Montraie to the mirror is 13.15 meters and the distance from the mirror to the base of the goalpost is also 13.15 meters. The height of Montraie's eyes above the mirror is 1.35 meters.

From the mirror's perspective, the image of the goalpost is reflected as if it were behind the mirror. The distance from the mirror to the image of the goalpost is also 13.15 meters, but in the opposite direction.

So, we can set up a right triangle with one leg of length 13.15 meters and the other leg of length 1.35 meters + h (the height of the goalpost). The hypotenuse of the triangle is the distance from Montraie's eyes to the top of the goalpost, which is the sum of the distances from Montraie to the mirror and from the mirror to the top of the goalpost, or 13.15 + 6.25 = 19.4 meters.

Using the Pythagorean theorem, we have:

(13.15)^2 + (1.35 + h)^2 = (19.4)^2

Simplifying and solving for "h", we get:

h = sqrt((19.4)^2 - (13.15)^2) - 1.35

h ≈ 3.43 meters

Therefore, the height of the goalpost is approximately 3.43 meters. Rounded to the nearest hundredth, the answer is 3.43 meters.