The shorter leg of a 30-60-90 triangle is 5.4 feet long. Find the perimeter
the opposite angle of the shorter leg is the smaller angle (which is the 30 degrees)
since in a 30-60-90 triangle, the hypotenuse is twice the shortest side, and the longer leg is sqrt(3) times the shortest side:
hypotenuse: 2*5.4 = 10.8 ft
longer side: sqrt(3)*5.4 = 9.353 ft
perimeter is just the sum of all lengths of the sides:
5.4 + 10.8 + 9.353 = 25.553 ft
hope this helps~ :)
the shorter leg of a 30-60-90 triangle is 2.4 inches long. find the perimeter.
The shorter leg + The shorter leg times 2 + The shorter leg times the square roots of 3.
2.4 + 4.8 + (2.4 times the square roots of 3)
2.4 + 4.8 + 4.16 = 11.36
To find the perimeter of a triangle, we need to add the lengths of all three sides. In a 30-60-90 triangle, the side lengths are related by a specific ratio.
In a 30-60-90 triangle, the ratio of the lengths of the sides is 1 : √3 : 2. The shorter leg (opposite the 30-degree angle) is represented by 1 in this ratio.
Given that the shorter leg is 5.4 feet long, we can set up a proportion to find the length of the other two sides:
1/5.4 = (√3)/x,
where x is the length of the longer leg.
To solve for x, we can cross-multiply:
1 * x = 5.4 * √3,
x = 5.4 * √3,
x ≈ 9.348 feet.
The length of the third side, which is the hypotenuse (opposite the 90-degree angle), can be found by multiplying the shorter leg by 2:
2 * 5.4 = 10.8 feet.
Now that we have the lengths of all three sides, we can find the perimeter by adding them together:
Perimeter = 5.4 + 9.348 + 10.8 = 25.548 feet.
Therefore, the perimeter of the triangle is approximately 25.548 feet.