Question

For a project in her Geometry class, Addison uses a mirror on the ground to measure

the height of her school's football goalpost. She walks a distance of 13.25 meters from
the goalpost, then places a mirror on flat on the ground, marked with an X at the
center. She then steps 1.3 meters to the other side of the mirror, until she can see the
top of the goalpost clearly marked in the X. Her partner measures the distance from
her eyes to the ground to be 1.55 meters. How tall is the goalpost? Round your answer
to the nearest hundredth of a meter.
1q
1.55 m
1.
13 m-
13.25 m

Answer 1

To find the height of the goalpost, we can use similar triangles. Addison's measurements can be used to set up a proportion and solve for x, the height of the goalpost.

Step-by-step explanation:

To find the height of the goalpost, we can use similar triangles. Let's call the height of the goalpost x. According to Addison's measurements, the distance from her eyes to the mirror is 1.3 meters and the distance from her eyes to the ground is 1.55 meters. Since the mirror is on the ground and Addison is looking at the top of the goalpost, we can set up the following proportion:

(1.3 meters) / x = (1.55 meters) / (x + 13.25 meters)

Cross multiplying, we get:

1.3(x + 13.25) = 1.55x

Simplifying the equation, we have:

1.3x + 17.225 = 1.55x

Subtracting 1.3x from both sides, we get:

0.25x = 17.225
Dividing both sides by 0.25, we find:

x = 68.9 meters

Therefore, the height of the goalpost is approximately 68.9 meters.

Answer 2

the height of the goalpost is approximately 10.48 meters.

Step-by-step explanation:

To find the height of the goalpost, Addison needs to use the distance from the mirror to the goalpost, the distance from her eyes to the ground, and the angle formed by the goalpost, the mirror, and her eyes. She can use the law of cosines to solve for the height of the goalpost.

Let "a" be the distance from the goalpost to the mirror, "b" be the distance from the mirror to Addison's eyes, and "c" be the distance from Addison's eyes to the ground.

The law of cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle formed by the goalpost, the mirror, and Addison's eyes.

In this case, a = 13.25 meters, b = 1.3 meters, and c = 1.55 meters. We can substitute these values into the formula to solve for the angle C:

1.55^2 = 13.25^2 + 1.3^2 - 2 * 13.25 * 1.3 * cos(C)

Solving for cos(C) and using the inverse cosine function (arccos), we find that C = 52.22 degrees.

Now that we know the angle C, we can use the law of sines to solve for the height of the goalpost. The law of sines states that:

sin(C) / a = sin(A) / h, where A is the angle formed by the ground, the mirror, and the goalpost, and h is the height of the goalpost.

In this case, A = 180 - C - 90 = 180 - 52.22 - 90 = 37.78 degrees, and a = 13.25 meters. We can substitute these values into the formula to solve for h:

sin(52.22) / 13.25 = sin(37.78) / h

Solving for h, we find that the height of the goalpost is approximately 10.48 meters.

Therefore, the height of the goalpost is approximately 10.48 meters.