2. Use the Pythagorean Theorem to solve the following:
A. A baseball diamond is a square of 90 feet on each side. How long is a throw from first
base to third base?
B. The bottom of a 25 foot plank is placed approximately 7 feet from the side of a barn.
Approximately how far up the barn wall will the plank reach?
a^2 + b^2 = c^2
90^2 + 90^2 = c^2
8,100 + 8,100 = c^2
16,200 = c^2
127.289 = c
Do the same for the next problem.
if the diagonal of square is 18cm,how long is a side?give a solution?
To solve these problems using the Pythagorean Theorem, you need to understand the relationship between the sides of a right triangle.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Let's solve the problems step by step:
A. To find the length of the throw from first base to third base on a baseball diamond:
1. Identify the right triangle formed by the first base, third base, and home plate. The sides of the triangle are the bases of the diamond.
2. The length of each side of the square baseball diamond is given as 90 feet.
3. The hypotenuse of the triangle (the throw from first base to third base) is the diagonal of the square. By realizing that the diagonal of a square divides it into two right triangles, you can apply the Pythagorean Theorem.
Using the Pythagorean Theorem,
c^2 = a^2 + b^2
where c is the length of the hypotenuse (throw from first base to third base), and a and b are the lengths of the other two sides (90 feet each).
c^2 = 90^2 + 90^2
Simplifying,
c^2 = 8100 + 8100
c^2 = 16200
Taking the square root of both sides,
c ≈ 127.28 feet
Therefore, the throw from first base to third base is approximately 127.28 feet.
B. To find the distance up the barn wall reached by a 25-foot plank placed 7 feet from the side of a barn:
1. Identify the right triangle formed by the plank, the distance up the barn wall, and the distance along the ground between the bottom of the plank and the barn.
2. The length of the plank is given as 25 feet, and the distance from the plank to the barn wall is given as 7 feet.
3. The hypotenuse of the right triangle is the distance up the barn wall, which we need to find.
Using the Pythagorean Theorem,
c^2 = a^2 + b^2
where c is the length of the hypotenuse (distance up the barn wall), and a and b are the lengths of the other two sides (25 feet and 7 feet, respectively).
c^2 = 25^2 + 7^2
Simplifying,
c^2 = 625 + 49
c^2 = 674
Taking the square root of both sides,
c ≈ 25.96 feet
Therefore, the plank will reach approximately 25.96 feet up the barn wall.