Solved on Dec 08, 2023

Yusuf uses a mirror to measure the height of his school building. He walks 13.95 m, places a mirror with an X, steps 2.15 m, and his eye height is 1.35 m. Find the school's height rounded to the nearest hundredth of a meter.

STEP 1

Assumptions
1. Yusuf walks 13.95 meters from the school and places a mirror on the ground.
2. He then steps 2.15 meters to the other side of the mirror.
3. The distance from Yusuf's eyes to the ground is 1.35 meters.
4. Yusuf can see the top of the school in the mirror when he is on the other side of it.
5. The problem can be modeled using similar triangles.

STEP 2

We will use the concept of similar triangles to solve this problem. The height of the school and the height of Yusuf's eyes form two similar triangles with the ground and the line of sight as their bases.

STEP 3

Let's denote the height of the school as $h$ meters. The distance from the school to the mirror is 13.95 meters, and the distance from the mirror to Yusuf's eyes is 2.15 meters.

STEP 4

The total distance from the school to Yusuf's eyes is the sum of the distance from the school to the mirror and from the mirror to Yusuf's eyes.
$Total\, distance = 13.95\, meters + 2.15\, meters$

STEP 5

Calculate the total distance.
$Total\, distance = 13.95\, meters + 2.15\, meters = 16.1\, meters$

STEP 6

The ratio of the height of the school to the total distance from the school to Yusuf's eyes is the same as the ratio of the height of Yusuf's eyes to the distance from the mirror to Yusuf's eyes.
$\frac{h}{16.1} = \frac{1.35}{2.15}$

STEP 7

Now, solve for $h$ by cross-multiplying.
$h \times 2.15 = 16.1 \times 1.35$

STEP 8

Calculate the right side of the equation.
$16.1 \times 1.35 = 21.735$

STEP 9

Now, divide both sides of the equation by 2.15 to isolate $h$ .
$h = \frac{21.735}{2.15}$

STEP 10

Calculate the height of the school.
$h = \frac{21.735}{2.15} \approx 10.11\, meters$

STEP 11

Round the answer to the nearest hundredth of a meter.
The height of the school is approximately $10.11$ meters.

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Yusuf uses a mirror to measure the height of his school building. He walks 13.95 m, places a mirror with an X, steps 2.15 m, and his eye height is 1.35 m. Find the school's height rounded to the nearest hundredth of a meter.

STEP 1

STEP 2

We will use the concept of similar triangles to solve this problem. The height of the school and the height of Yusuf's eyes form two similar triangles with the ground and the line of sight as their bases.

STEP 3

Let's denote the height of the school as $h$ meters. The distance from the school to the mirror is 13.95 meters, and the distance from the mirror to Yusuf's eyes is 2.15 meters.

STEP 4

The total distance from the school to Yusuf's eyes is the sum of the distance from the school to the mirror and from the mirror to Yusuf's eyes.
$Total\, distance = 13.95\, meters + 2.15\, meters$

STEP 5

Calculate the total distance.
$Total\, distance = 13.95\, meters + 2.15\, meters = 16.1\, meters$

STEP 6

The ratio of the height of the school to the total distance from the school to Yusuf's eyes is the same as the ratio of the height of Yusuf's eyes to the distance from the mirror to Yusuf's eyes.
$\frac{h}{16.1} = \frac{1.35}{2.15}$

STEP 7

Now, solve for $h$ by cross-multiplying.
$h \times 2.15 = 16.1 \times 1.35$

STEP 8

Calculate the right side of the equation.
$16.1 \times 1.35 = 21.735$

STEP 9

Now, divide both sides of the equation by 2.15 to isolate $h$ .
$h = \frac{21.735}{2.15}$

STEP 10

Calculate the height of the school.
$h = \frac{21.735}{2.15} \approx 10.11\, meters$

STEP 11

Round the answer to the nearest hundredth of a meter.
The height of the school is approximately $10.11$ meters.

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Yusuf uses a mirror to measure the height of his school building. He walks 13.95 m, places a mirror with an X, steps 2.15 m, and his eye height is 1.35 m. Find the school's height rounded to the nearest hundredth of a meter.

STEP 1

STEP 2

We will use the concept of similar triangles to solve this problem. The height of the school and the height of Yusuf's eyes form two similar triangles with the ground and the line of sight as their bases.

STEP 3

Let's denote the height of the school as h h h meters. The distance from the school to the mirror is 13.95 meters, and the distance from the mirror to Yusuf's eyes is 2.15 meters.

STEP 4

The total distance from the school to Yusuf's eyes is the sum of the distance from the school to the mirror and from the mirror to Yusuf's eyes.Total distance=13.95 meters+2.15 metersTotal\, distance = 13.95\, meters + 2.15\, metersTotaldistance=13.95meters+2.15meters

STEP 5

Calculate the total distance.Total distance=13.95 meters+2.15 meters=16.1 metersTotal\, distance = 13.95\, meters + 2.15\, meters = 16.1\, metersTotaldistance=13.95meters+2.15meters=16.1meters

STEP 6

The ratio of the height of the school to the total distance from the school to Yusuf's eyes is the same as the ratio of the height of Yusuf's eyes to the distance from the mirror to Yusuf's eyes.h16.1=1.352.15\frac{h}{16.1} = \frac{1.35}{2.15}16.1h​=2.151.35​

STEP 7

Now, solve for h h h by cross-multiplying.h×2.15=16.1×1.35h \times 2.15 = 16.1 \times 1.35h×2.15=16.1×1.35

STEP 8

Calculate the right side of the equation.16.1×1.35=21.73516.1 \times 1.35 = 21.73516.1×1.35=21.735

STEP 9

Now, divide both sides of the equation by 2.15 to isolate h h h.h=21.7352.15h = \frac{21.735}{2.15}h=2.1521.735​

STEP 10

Calculate the height of the school.h=21.7352.15≈10.11 metersh = \frac{21.735}{2.15} \approx 10.11\, metersh=2.1521.735​≈10.11meters

STEP 11

Round the answer to the nearest hundredth of a meter.The height of the school is approximately 10.11 10.11 10.11 meters.

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Let's denote the height of the school as $h$ meters. The distance from the school to the mirror is 13.95 meters, and the distance from the mirror to Yusuf's eyes is 2.15 meters.

The total distance from the school to Yusuf's eyes is the sum of the distance from the school to the mirror and from the mirror to Yusuf's eyes.
$Total\, distance = 13.95\, meters + 2.15\, meters$

Calculate the total distance.
$Total\, distance = 13.95\, meters + 2.15\, meters = 16.1\, meters$

The ratio of the height of the school to the total distance from the school to Yusuf's eyes is the same as the ratio of the height of Yusuf's eyes to the distance from the mirror to Yusuf's eyes.
$\frac{h}{16.1} = \frac{1.35}{2.15}$

Now, solve for $h$ by cross-multiplying.
$h \times 2.15 = 16.1 \times 1.35$

Calculate the right side of the equation.
$16.1 \times 1.35 = 21.735$

Now, divide both sides of the equation by 2.15 to isolate $h$ .
$h = \frac{21.735}{2.15}$

Calculate the height of the school.
$h = \frac{21.735}{2.15} \approx 10.11\, meters$

Round the answer to the nearest hundredth of a meter.
The height of the school is approximately $10.11$ meters.