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A boat is floating out at sea. You are standing on a cliff. You are standing 3 meters

from the edge of the cliff. You are 1.5 meters tall and the cliff is 10 meters high. How

far is the boat from the cliff? (CD).

A boat is floating out at sea You are standing on a cliff You are standing 3 meters from the edge of the cliff You

Answer :

The distance between the boat and the cliff (CD) is 20 meters.

To find the distance between the boat and the cliff (CD), we can use the concept of similar triangles.

Let's denote:

- AB as the height of the cliff (10 meters).

- AC as the distance from the cliff to the boat.

- AD as the distance from the cliff edge to your feet (3 meters).

- AE as your height (1.5 meters).

From the information provided, we have:

- AB = 10 meters

- AD = 3 meters

- AE = 1.5 meters

Since we have a right triangle formed by your height (AE), your distance from the cliff (AD), and the distance from the cliff to the boat (AC), we can use the property of similar triangles.

The ratio of corresponding sides in similar triangles is equal. Therefore:

[tex]\[\frac{AE}{AB} = \frac{AD}{AC}\][/tex]

Plugging in the values:

[tex]\[\frac{1.5}{10} = \frac{3}{AC}\][/tex]

Cross-multiplying:

[tex]\[1.5 \times AC = 3 \times 10\]\[AC = \frac{3 \times 10}{1.5} = 20\][/tex]

So, the distance between the boat and the cliff (CD) is 20 meters.

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Rewritten by : Barada