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

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) (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) (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: ::

That means the shorter leg is half the length of the hypotenuse and the longer leg is times the hypotenuse. And the long leg is then times the short leg.

Here your long leg is , so the short leg, and the height of the triangle must be .

Therefore your area is given by:

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

Assumption: The shorter leg is the base:

Here your short leg is , so the long leg, and the height of the triangle must be .

Therefore your area is given by:

Makes a difference by a factor of 3.
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