SOLUTION: Please help with this question. Determine the area of the triangle to the nearest tenth. Use A=bh/2. It is a right triangle 30-60-90 and the base measure is 6squareroot3. The

Algebra ->  Triangles -> SOLUTION: Please help with this question. Determine the area of the triangle to the nearest tenth. Use A=bh/2. It is a right triangle 30-60-90 and the base measure is 6squareroot3. The       Log On


   

Question 135988: Please help with this question. Determine the area of the triangle to the nearest tenth. Use A=bh/2. It is a right triangle 30-60-90 and the base measure is 6squareroot3. The height is not given. Thank you
Found 2 solutions by nycsharkman, solver91311:
Answer by nycsharkman(136) About Me  (Show Source):
You can put this solution on YOUR website!
Please help with this question. Determine the area of the triangle to the nearest tenth. Use A=bh/2. It is a right triangle 30-60-90 and the base measure is 6squareroot3. The height is not given.
Area = base times height divided by 2
It's a 30-60-90 triangle.
In this type of triangle, 30 degrees is opposite a, 90 degrees is opposite 2a and 60 degrees is opposite a times the square root 3, which is written a(sqrt{3}). The value of a here is the number 6 in front of square root 3 in the given base.
The base is 6(sqrt{3}), which tells me the value of a is 6.
Since 30 degrees is opposite the height of the triangle and a = 6, then the height is 6.
A = [6(sqrt{3}) times 6]/2
A = 36(sqrt{3})/2
A = 18(sqrt{3})
Is this clear?


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The trouble is, you didn't specify which of the triangle legs you are calling the base.

Assumption: The longer leg is the base:



A 30-60-90 triangle has sides in the following proportion: 1%2F2:sqrt%283%29%2F2:1

That means the shorter leg is half the length of the hypotenuse and the longer leg is sqrt%283%29%2F2 times the hypotenuse. And the long leg is then sqrt%283%29 times the short leg.

Here your long leg is 6sqrt%283%29, so the short leg, and the height of the triangle must be 6sqrt%283%29%2Fsqrt%283%29=6.

Therefore your area is given by: A=%286%2A6sqrt%283%29%29%2F2=18sqrt%283%29

==============================================================

Assumption: The shorter leg is the base:



Here your short leg is 6sqrt%283%29, so the long leg, and the height of the triangle must be 6sqrt%283%29%2Asqrt%283%29=6%2A3=18.

Therefore your area is given by: A=%2818%2A6sqrt%283%29%29%2F2=54sqrt%283%29

Makes a difference by a factor of 3.