given triangle abc, measure of angle b= 120 degrees, ab= 6 units, bc= 10 units, find the area of abc
To find the area of triangle ABC, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, we need to find the height of triangle ABC.
First, let's draw triangle ABC and label the given information:
```
C
/ \
/ \
6 / \ 10
/ \
/_________\
A 120° B
```
We know that AB = 6 units and BC = 10 units, and angle B = 120 degrees.
To find the height of the triangle, we can use trigonometry.
Since angle B is an angle opposite side AC, we can use the sine function:
sin(B) = opposite / hypotenuse
sin(120°) = height / 6
To find the value of sin(120°), we can use the fact that sin(120°) = sin(180° - 120°) = sin(60°).
sin(60°) = sqrt(3) / 2 (approximately 0.866).
Now we can solve for the height:
0.866 = height / 6
height = 0.866 * 6
height ≈ 5.196 units
Now that we have the height, we can find the area:
Area = (1/2) * base * height
Area = (1/2) * 10 * 5.196
Area ≈ 25.98 square units
Therefore, the area of triangle ABC is approximately 25.98 square units.
Area = 0.5*AB*BC*sinB.
Area = 0.5*6*10*sin120 = 26 Sq. Units.