What is the area of a 30-60-90 triangle with hypotenuse length of 48 in.

Hi,

If the hypotenuse is 48 in., then the side across from the 30 degree angle is 24 in., and the side across from the 60 degree angle is 24√3 in.

Area = 1/2(24)(24√3) = 288√3 square inches <==ANSWER

I hope that helps!! :-)

In a 30-60-90 triangle, the ratio of the length of the hypotenuse to the length of the short leg is 2:1. Therefore, the length of the short leg is 24 in.

In a 30-60-90 triangle, the ratio of the length of the short leg to the length of the long leg is 1:sqrt 3
Therefore, the length of the long leg is 24(sqrt 3) in.

(Note that "sqrt 3" means "square root of 3")

The short and long legs form a right angle, so you can use the following area formula:

Area of a Triangle = (1/2)(Base)(Height) = (1/2)(24)(24sqrt3) = 288(sqrt3) square inches

Note that the two legs of the triangle are the base and height of the triangle, so if we can find the two legs, we can use A = (1/2)bh to find the area.

The sides in a 30-60-90 triangle are in ratio 1:√3:2. So, the two legs are 48/2 = 24 and (√3/2)(48) = 24√3. Therefore, the area if the triangle is:
A = (1/2)bh
= (1/2)(24)(24√3)
= 288√3 in^2.

I hope this helps!

area = (b*h) div 2
cos 30 = adj div 48 inch
48cos30=adj
adj=41.5
sin30=opp div 48 inch
opp=24

area = 41.5 * 24 div 2
996 div 2
area = 498 inches^2

Q 32 15 (oYo)