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 is the cliff? Assume the two triangles are similar.
Postscript: The distance from the tent to the cliff is 400 feet. (for those of you that have Stretching and Shrinking 7th grade math book, it is question 25 on page 68)
1.5to1
To find the approximate height of the tall cliff, we can use the concept of similar triangles. Let's break down the problem and explain the steps to solve it.
Step 1: Understand the given information.
- Judy lies on the ground 45 feet away from her tent.
- The height of her tent is 10 feet.
- The tent and the cliff are in Judy's line of sight.
- The distance between the tent and the cliff is 400 feet.
Step 2: Identify the triangles involved.
In this problem, there are two triangles: the small triangle formed by Judy, her tent, and the distance to the tent, and the large triangle formed by Judy, the cliff, and the distance between them.
Step 3: Recognize the similarity between the triangles.
The problem states that the two triangles are similar. This means that their corresponding angles are congruent, and the ratio of their corresponding sides is constant.
Step 4: Set up the proportion.
Since the triangles are similar, we can set up a proportion to find the height of the cliff.
Let's call the height of the cliff "h".
The proportion would be:
(tent height) / (distance to the tent) = (cliff height) / (distance to the cliff)
Substituting the given values:
10 / 45 = h / 400
Step 5: Solve the proportion.
Now we can solve the proportion to find the height of the cliff.
Cross-multiplying the proportion:
10 * 400 = 45h
Dividing both sides by 45:
4000 = 45h
Dividing both sides by 45:
h ≈ 88.89 (rounded to two decimal places)
Step 6: Answer the question.
Therefore, the approximate height of the cliff is approximately 88.89 feet.
Please note that the answer is an approximation since we rounded the value to two decimal places based on the given information.
30 feet
According to my diagram,
h/445 = 10/45
h = 10(445)/45
= ...