Anne wants to tie a support line from the top of a 50 foot radio tower to an anchor spot 30 feet from the tower’s base. Approximately how long will the line need to be?
This makes a right angle triangle -- and can be solved by the Pythagorean Theorem.
a^2 + b^2 = c^2
50^2 + 30^2 = c^2
2500 + 900 = c^2
3400 = c^2
58.3 = c
Well, it seems like Anne's got some ambitious plans to tie a support line! Let's do a little bit of math here. We can pretend that the line, the distance from the tower's top to the anchor spot, and the distance from the tower's base to the anchor spot form a right triangle. So using good ol' Pythagoras' Theorem (a² + b² = c²), we can calculate the length of the line.
In this case, "a" represents the height of the tower which is 50 feet, and "b" represents the distance from the tower's base to the anchor spot which is 30 feet. So, by plugging these values into our equation, we get:
50² + 30² = c²
2500 + 900 = c²
3400 = c²
So the line will need to be √3400 feet long approximately. Now, I could calculate this for you, but let's be real, nobody likes square roots, right? So just grab a calculator and do that part yourself! Happy measuring, my friend!
To determine the length of the support line, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (hypotenuse).
In this case, the height of the radio tower is one side of the right triangle, and the distance from the tower's base to the anchor spot is the other side. The support line will act as the hypotenuse of this triangle.
Let's denote the height of the radio tower as 'a' and the distance from the base to the anchor spot as 'b'.
According to the Pythagorean theorem:
a^2 + b^2 = c^2
In this case, a = 50 ft and b = 30 ft.
Plugging the values into the equation:
(50)^2 + (30)^2 = c^2
Simplifying:
2500 + 900 = c^2
3400 = c^2
To solve for c, we take the square root of both sides:
√3400 = c
Approximately, the length of the support line will be:
c ≈ 58.31 ft
Therefore, the support line will need to be approximately 58.31 feet long.
To determine the length of the support line, we can use the Pythagorean Theorem. According to the theorem, in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the radio tower represents one side of the right triangle, and the distance from the tower's base to the anchor spot represents the other side. The support line will act as the hypotenuse.
Let's calculate the length of the support line:
1. Square the height of the radio tower: 50^2 = 2500.
2. Square the distance from the tower's base to the anchor spot: 30^2 = 900.
3. Add the squared values together: 2500 + 900 = 3400.
4. Finally, take the square root of the sum to get the length of the support line: √3400 ≈ 58.3 feet.
Therefore, the support line will need to be approximately 58.3 feet long.