Judy lies on the ground 45 feet from her tent. Both the top of the tent and the top of a tall cliff are in her line of sight. Her tent is 10 feet tall. About how high is the cliff? Assume the two triangles are similar?

Question

Mason Adams · Accepted Answer

There is insufficient information to answer this question.

We would need to know how far Judy was from the base of the cliff (or some equivalent information).

Aaliyah Anderson · Answer

undefined To find the height of the cliff, we can set up a proportion based on the similar triangles formed by Judy's line of sight to the top of her tent and the top of the tall cliff. Using the given information, we have:

Height of the tent = 10 feet
Distance from Judy to the tent = 45 feet
Unknown height of the cliff = $ x $ feet

Using the similarity of the triangles, we can set up the proportion:

$$
\frac{{\text{Height of the tent}}}{{\text{Distance from Judy to the tent}}} = \frac{{\text{Height of the cliff}}}{{\text{Distance from Judy to the cliff}}}
$$

Plugging in the values we have:

$$
\frac{{10 \text{ feet}}}{{45 \text{ feet}}} = \frac{{x \text{ feet}}}{{\text{Distance from Judy to the cliff}}}
$$

Solving for $ x $, we get:

$$
x = \frac{{10 \text{ feet} \times \text{Distance from Judy to the cliff}}}{{45 \text{ feet}}}
$$

Since we do not have the exact distance from Judy to the cliff, we cannot calculate the precise height of the cliff. However, using this proportion, you can find the height of the cliff if you know the distance from Judy to the cliff.