What is the perimeter of a 30 60 90 triangle whose shorter leg is 5 inches long?
5,10,5*sqrt3 add them
To find the perimeter of a triangle, we need to add up the lengths of all its sides.
A 30-60-90 triangle is a special right triangle where the angles of the triangle are 30 degrees, 60 degrees, and 90 degrees. In this triangle, the ratio of the sides is 1:√3:2.
Since the shorter leg is 5 inches, we can use this ratio to find the lengths of the other two sides.
The shorter leg in our case is 5, so the longer leg (opposite the 60-degree angle) is 5 * √3, and the hypotenuse (opposite the 90-degree angle) is 2 * 5 = 10.
Now, we can find the perimeter by adding up the lengths of all the sides: 5 + 5 * √3 + 10 = 5 + 5√3 + 10.
Therefore, the perimeter of the 30-60-90 triangle with a shorter leg of 5 inches is 15 + 5√3 inches.