Answer:
Explanation:
To find the distance from the midpoint of one side to the opposite vertex of an equilateral triangle, you can use the properties of an equilateral triangle. In an equilateral triangle, all sides are equal in length and all angles are equal to 60 degrees.
Given that the side of the triangle is 1450 feet long, we can find the length from the midpoint of one side to the opposite vertex using the following steps:
1. Divide the side length by 2 to find the length of one half of the side: 1450 feet ÷ 2 = 725 feet.
2. Use the Pythagorean theorem to find the length from the midpoint to the opposite vertex. In a right triangle formed by the midpoint, the opposite vertex, and the midpoint of the base, the hypotenuse (opposite vertex to midpoint) is the side length of the equilateral triangle, and the two legs are the half of the side length.
a. The hypotenuse is the side length of the equilateral triangle, which is 1450 feet.
b. One leg is half of the side length, which is 725 feet.
c. The other leg is the distance from the midpoint to the opposite vertex.
Applying the Pythagorean theorem:
(725 feet)^2 + (leg length)^2 = (1450 feet)^2
525,625 + (leg length)^2 = 2,102,500
(leg length)^2 = 2,102,500 - 525,625
(leg length)^2 = 1,576,875
Taking the square root of both sides, we get:
leg length = √1,576,875
leg length ≈ 1256.74 feet
Therefore, the distance from the midpoint of one side to the opposite vertex of the equilateral triangle is approximately 1256.74 feet.