In the triangle ABC., BC = 12cm, ABC = 80 degree and ACB = 30 degree
Calculate the area of triangle ABC.
angle BAC = 180-80-30 = ....
now find AB using the Sine Law.
Area of triangle = (1/2)(AB)(BC)sin80° = ....
you do the button-pushing.
Let me know what you get.
sin70/a = sin80/12
To calculate the area of triangle ABC, we can use the formula for the area of a triangle which is A = 1/2 * base * height.
However, in this case, we don't have the height of the triangle given directly. But we can use the given information to find the height using trigonometry.
First, let's label the triangle as follows:
A is the vertex angle of the triangle.
B is one of the base angles.
C is the other base angle.
We are given:
BC = 12 cm, which is the length of the side opposite angle A.
ABC = 80 degrees, which is angle A.
ACB = 30 degrees, which is one of the base angles, either angle B or angle C.
To find the height, we need to find the length of the altitude from A to BC.
To find this height, we can use the trigonometric ratio for finding the height of an equilateral triangle:
In an equilateral triangle, all angles are 60 degrees, and all sides are equal.
The height of an equilateral triangle can be found using the formula: height = (side length * √3) / 2
But in this case, we have an isosceles triangle, not an equilateral triangle. However, we can take advantage of the fact that angle B equals angle C (since it is an isosceles triangle), and use the same formula.
So, the height (h) of the triangle ABC is given by:
h = (BC * √3) / 2
Substituting the given value:
h = (12 cm * √3) / 2
Now that we have the height of the triangle, we can use the formula for the area of a triangle to find the area (A):
A = 1/2 * (base) * (height)
A = 1/2 * (BC) * (h)
Substituting the given value and the value of height (h) we found:
A = 1/2 * (12 cm) * ((12 cm * √3) / 2)
Simplifying the expression:
A = 6 cm * 12 cm * √3
A = 72 cm² * √3
Therefore, the area of triangle ABC is 72 cm² * √3.