The Vietnam Veterans Memorial in Washington, D.C., is made up of two walls, each 246.75 feet long, that meet at an angle of 125.2°. Find, to the nearest foot, the distance between the ends of the walls that do not meet.
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Law of cosines
c^2 = a^2+ b^2 - 2 a b cos C
Because this is an isosceles triangle, B and C are both 27.4°
To find the distance between the ends of the walls that do not meet, we can use trigonometry and the given information about the angle and length of the walls.
1. Draw a diagram: Sketch a representation of the two walls meeting at an angle of 125.2°.
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wall 1
wall 2
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2. Split the angle: Since we need to find the distance between the ends of the walls that do not meet, we can split the angle of 125.2° into two angles of 62.6° each.
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\(62.6°)|
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wall 1
wall 2
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(62.6°)
3. Use trigonometry: We will use the cosine function to find the length of the side opposite to the split angle (62.6°), which represents the distance between the ends of the walls.
cos(62.6°) = adjacent side / hypotenuse
Let x be the distance between the ends of the walls.
cos(62.6°) = x / 246.75
4. Solve for x: Rearrange the equation to solve for x.
x = cos(62.6°) * 246.75
5. Calculate the distance: Substitute the value of cos(62.6°) into the equation and solve for x.
x ≈ 0.4652 * 246.75
x ≈ 114.6 feet
Therefore, to the nearest foot, the distance between the ends of the walls that do not meet is approximately 115 feet.