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 tall is the cliff?
To determine the approximate height of the cliff, we can use similar triangles.
Step 1: Draw a diagram representing the situation.
- Draw a line segment from the top of the tent to the top of the cliff.
- Label the distance from Judy's position to the tent as 45 feet.
- Label the height of the tent as 10 feet.
Step 2: Identify the similar triangles.
- We have two right triangles: one formed by Judy's line of sight, the tent, and the ground, and another formed by Judy's line of sight, the cliff, and the ground.
- The two triangles have a shared angle at Judy's position, and both are right triangles.
Step 3: Set up a proportion.
- Since the triangles are similar, the corresponding sides are proportional.
- Let 'x' represent the height of the cliff.
- The proportion can be set up as follows: (height of the cliff) / (distance to the tent) = (height of the tent) / (distance to the tent)
Step 4: Solve the proportion and find the value of 'x'.
- Simplify the proportion: x / 45 = 10 / 45.
- Cross-multiply to get x = (10 * 45) / 45.
- Calculate x: x = 10.
Therefore, the approximate height of the cliff is 10 feet.
To find the height of the cliff, we can use similar triangles since both the top of the tent and the top of the cliff are in Judy's line of sight.
Let's assume the height of the cliff is 'x' feet.
According to the similar triangles, the ratio of the height of the cliff to the distance from Judy to the cliff is equal to the ratio of the height of the tent to the distance from Judy to the tent.
So, we can set up the ratio:
x/45 = 10/45
To solve for 'x', we can cross-multiply:
x * 45 = 10 * 45
x = 10
Therefore, the height of the cliff is approximately 10 feet.