Two poles of lengths 10 ft. and 15 ft. are set up vertically with their bases on horizontal ground 12 ft apart. Find the distance between the tops of the poles.
I got 7.53 ft is this right, if not can you explain and post solution
the distance is √(12^2+(15-10)^2) = 13
Maybe you should have shown your work.
To find the distance between the tops of the poles, we can use the Pythagorean theorem. Let's label the shorter pole as A, the longer pole as B, and the distance between their bases as C (which is 12 ft).
According to the Pythagorean theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the distance between the tops of the poles is the hypotenuse of a right triangle.
Using the theorem, we have:
\[A^2 + B^2 = C^2\]
Plugging in the values we know:
\[10^2 + 15^2 = 12^2\]
\[100 + 225 = 144\]
\[325 \neq 144\]
Therefore, the distance you calculated, 7.53 ft, is not correct.
To find the correct distance between the tops of the poles, we need to use the correct formula:
\[A^2 + B^2 = C^2\]
\[10^2 + 15^2 = C^2\]
\[100 + 225 = C^2\]
\[325 = C^2\]
\[C = \sqrt{325}\]
\[C \approx 18.02\]
Therefore, the distance between the tops of the poles is approximately 18.02 ft.
To solve this problem, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance between the tops of the poles forms the hypotenuse, and the poles themselves form the other two sides of a right triangle.
Let's label the length of the first pole as A (10 ft), the length of the second pole as B (15 ft), and the distance between their bases as C (12 ft).
To find the distance between the tops of the poles, let's call it D, we can create two right triangles:
1. Triangle ABC: The sides are A, B, and C.
2. Triangle ADB: The sides are A, D, and B.
According to the Pythagorean theorem, we have two equations:
1. A^2 + C^2 = AC^2
2. A^2 + D^2 = B^2
Let's solve these equations step-by-step:
1. A^2 + C^2 = AC^2
Plugging in the values:
10^2 + 12^2 = AC^2
100 + 144 = AC^2
244 = AC^2
Taking the square root of both sides:
√244 = AC
AC ≈ 15.62 ft
2. A^2 + D^2 = B^2
Plugging in the values:
10^2 + D^2 = 15^2
100 + D^2 = 225
D^2 = 225 - 100
D^2 = 125
Taking the square root of both sides:
√D^2 ≈ √125
D ≈ 11.18 ft
Therefore, the distance between the tops of the poles, D, is approximately 11.18 ft, not 7.53 ft.
Please note that if you got a different answer, there may have been a mistake in your calculations or substitutions. Double-check your work to ensure accuracy.