ok,judy lies on the ground 45 feet from her tent. both the top of the tent and the top of the cliffare in her line of sight. her tent is 10 feet tall. about how high is the cliff
one more piece of information is needed.
once you have that, set up a ration using similar triangles.
e.g, if we knew she was 200 feet from the base of the cliff, we could say :
h/200 = 10/45 and solve for h
To determine the approximate height of the cliff, we can use the concept of similar triangles. The ratio of the height of the tent to the distance from the tent is the same as the ratio of the height of the cliff to the same distance.
Let's solve it step by step:
Step 1: Identify the given information:
- Distance from Judy to her tent: 45 feet
- Height of Judy's tent: 10 feet
Step 2: Set up the proportion:
We'll use the following proportion:
(height of the cliff) / (distance from Judy to the cliff) = (height of the tent) / (distance from Judy to the tent)
Let's substitute the values we know:
(cliff height) / (distance to cliff) = 10 ft / 45 ft
Step 3: Simplify the proportion:
Simplifying the proportion gives us:
(cliff height) / (distance to cliff) = 2 / 9
Step 4: Find the cliff height:
To find the height of the cliff, we need to find the value of (cliff height). We can do this by cross-multiplying and solving the equation.
(cliff height) = (distance to cliff) * (2 / 9)
Since we don't know the exact distance from Judy to the cliff, we can only provide an approximation using the given information.
Let's assume the distance to the cliff is approximately 100 feet:
(cliff height) = 100 ft * (2 / 9)
(cliff height) ≈ 22.22 feet
Therefore, based on the assumption that the distance to the cliff is 100 feet, the approximate height of the cliff is around 22.22 feet.