A person who is 6 feet tall walks away from a flagpole toward the tip of the shadow of the flagpole. When the person is 32 feet from the flagpole, the tips of the person's shadow and the shadow cast by the flagpole coincide at a point 4 feet in front of the person.
Therefore making the answer 54?
Is there a question in this story?
I assume you want to know the height of the flagpole.
Since we have similar triangles, use a simple ratio ....
h/36 = 6/4
etc
Step 1: Let's assume the height of the flagpole is x feet.
Step 2: The person's height is given as 6 feet.
Step 3: When the person is 32 feet from the flagpole, the tips of the person's shadow and the flagpole's shadow coincide at a point 4 feet in front of the person.
Step 4: This means that the person's shadow and the flagpole's shadow are both (32 + 4) = 36 feet long at that point.
Step 5: Using similar triangles, we can set up a proportion to find the height of the flagpole.
Step 6: The proportion can be set up as (6 feet) / (person's shadow length) = (x feet) / (flagpole's shadow length).
Step 7: Plugging in the values, we get (6 feet) / (36 feet) = (x feet) / (36 feet).
Step 8: Cross-multiplying, we have 6 * 36 = 36 * x.
Step 9: Simplifying, we find 216 = 36x.
Step 10: Dividing both sides by 36, we get x = 216 / 36 = 6 feet.
Step 11: Therefore, the height of the flagpole is 6 feet.
To find the height of the flagpole, we can set up a proportion using similar triangles. Let's assign some variables:
Let x represent the height of the flagpole.
Let y represent the length of the person's shadow.
Since the person is 6 feet tall, we know their shadow is also 6 feet. Let's write the proportion:
(x / y) = (6 / 6)
Now, we need to find the length of the flagpole's shadow. Since we know the person's shadow and the point at which the shadows coincide, we can set up another proportion:
(y + 4) / (y) = (x) / (y + 32)
We can combine these two equations to solve for x:
(x / y) = (6 / 6)
(x) = (6y) ---- Equation (1)
Substitute Equation (1) into the other proportion:
(y + 4) / (y) = (6y) / (y + 32)
Now, we can cross-multiply and solve for y:
(y + 4)(y + 32) = (6y)(y)
(y^2 + 36y + 128) = (6y^2)
0 = 6y^2 - y^2 - 36y - 128
5y^2 - 36y - 128 = 0
To solve this quadratic equation, you can use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 5, b = -36, and c = -128. Plug these values into the quadratic formula to find the values of y.
Once you find the value of y, substitute it back into equation (1) to find the value of x, which represents the height of the flagpole.