How would I find the height of the clocktower using this information?
Bobby, who is 5’6” tall, took a square of paper, folded it in half and then taped a straw to the hypotenuse. Then holding the bottom of the paper level, he walked back from the clocktower until he could sight the top of the clocktower through the straw. At that point he was 42 feet from the clocktower. He also noted his shadow was 8 ft long. 2 hrs later, he came back and measured the clocktower’s shadow and it was 20 ft long.
What is your question?
My question is:
"How would I find the height of the clocktower using this information?" as well as "What is the height of the clocktower?
Confusing wording.
Since you are sighting through the straw, the straw forms the hypotenuse.
You can sketch 2 similar triangles and form ratios
Bobby's height / length of Bobby's shadow = height of tower/tower shadow
5.5/8 = h/(42+8)
8h = 5.5(50)
h = 34.375
The fact that "2 hrs later, he came back and measured the clocktower’s shadow and it was 20 ft long." has nothing to do with it.
To find the height of the clocktower, we can use similar triangles and the concept of proportions. Let's break down the steps to determine the height:
Step 1: Determine the length of Bobby's standing height.
- Bobby's height is given as 5'6". Convert this height to inches: 5 feet * 12 inches + 6 inches = 66 inches. So, Bobby's standing height is 66 inches.
Step 2: Calculate the length of Bobby's shadow.
- Bobby measured his shadow to be 8 feet. Convert this length to inches: 8 feet * 12 inches = 96 inches. So, the length of Bobby's shadow is 96 inches.
Step 3: Calculate the distance Bobby walked from the clocktower.
- Bobby walked 42 feet away from the clocktower.
Step 4: Determine the length of the clocktower's shadow two hours later.
- After 2 hours, Bobby measured the clocktower's shadow to be 20 feet.
Step 5: Calculate the height of the clocktower using the concept of similar triangles.
- Let's set up a proportion using the similar triangles formed by Bobby and the clocktower:
Height of Clocktower / Length of Clocktower's Shadow = Bobby's Height / Bobby's Shadow
Let's substitute the given values:
Height of Clocktower / 20 ft = 66 inches / 96 inches
Now, solve for the height of the clocktower:
Height of Clocktower = (20 ft * 66 inches) / 96 inches
Calculate the height to get the final answer.
So, by using the given measurements and proportions, you can calculate the height of the clocktower.