The hypotenuse of a 30-60-90 triangle is 10. Find the perimeter.
How do i do that?
The sides of a 30-60-90 triangle are in the ratio of
1 : √3 : 2
so your triangle will be in the ratio a : b : 10
a/1 = 10/2
a = 5
b/√3 = 10/2
b = 5√3
so the perimeter = 5 + 5√3 + 10 = 15 + 5√3 or appr. 23.66
how would you find the area
To find the perimeter of a triangle, you need to add the lengths of all three sides. In the case of a 30-60-90 triangle, where the angles measuring 30 degrees, 60 degrees, and 90 degrees, we can determine the lengths of the sides using ratio.
In a 30-60-90 triangle, the relationship between the lengths of the sides is as follows:
- The side opposite the 30-degree angle (short leg) is half the length of the hypotenuse.
- The side opposite the 60-degree angle (long leg) is (√3 / 2) times the length of the hypotenuse.
- The hypotenuse is the longest side and is opposite the 90-degree angle.
Given that the hypotenuse is 10, we can determine the lengths of the other sides:
- The short leg is half the length of the hypotenuse: 10 / 2 = 5.
- The long leg is (√3 / 2) times the length of the hypotenuse: (√3 / 2) * 10 = 5√3.
Now we can calculate the perimeter by adding the lengths of all three sides:
Perimeter = 5 + 5√3 + 10.
Hence, the perimeter of the triangle is 15 + 5√3 units.