Finding a triangles angles from its area + 2 sides

In summary, the formula for finding the angles of a triangle from its area and 2 sides is A = (1/2)bh, where A is the area, b is the base, and h is the height. This formula can be used for any type of triangle as long as the area and two sides are known. If you only have the area and one side, you will not be able to find the angles using this formula. The unit of measurement for the area and sides can be any unit of length. There is no specific order in which the values should be inputted into the formula.
  • #1
rought
34
0

Homework Statement



A triangle had area of 21 cm² and two of its sides are 9 cm and 14cm long.
Find the possible measures of the angle formed by these sides?


Homework Equations



Area= 1/2abSin(C)

The Attempt at a Solution



1/2 (9)(14)Sin C = 21 --> Sin C = (1/3)

approx 19.5 or 160.5


I'm just not sure if i did it right does this seem correct?
 
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  • #2
rought said:
I'm just not sure if i did it right does this seem correct?
Seems correct.
 
  • #3


Your approach to solving for the angle formed by the given sides is correct. However, there are two possible angles that could satisfy the given conditions. As you have calculated, one angle is approximately 19.5 degrees and the other is approximately 160.5 degrees. This is because the sine function has two possible solutions for a given value. Therefore, in this case, the possible measures of the angle formed by the given sides are 19.5 degrees and 160.5 degrees. It is important to note that this solution assumes the triangle is a non-right triangle. If the triangle is a right triangle, then one of the angles will be 90 degrees and the other two angles can be found using the Pythagorean theorem.
 

FAQ: Finding a triangles angles from its area + 2 sides

What is the formula for finding the angles of a triangle from its area and 2 sides?

The formula for finding the angles of a triangle from its area and 2 sides is A = (1/2)bh, where A is the area of the triangle, b is the base, and h is the height.

Can I find the angles of any triangle using this formula?

Yes, this formula can be used to find the angles of any triangle, as long as you have the area and two sides of the triangle.

What if I have the area and only one side of the triangle?

In order to find the angles of a triangle, you need at least two sides. If you have the area and only one side, you will not be able to find the angles using this formula.

What is the unit of measurement for the area and sides in this formula?

The unit of measurement for the area and sides in this formula can be any unit of length, such as meters, centimeters, or feet.

Is there a specific order in which I should input the values into the formula?

No, there is no specific order in which you should input the values into the formula. As long as you have the area and two sides, you can input them in any order and still get the correct angles.

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