#### Question

# Given: Δ ABC. B = 130 degrees, a = 2, b = 6. Find the area of the triangle.?

please help!

#### Answers

Recall that the area of a triangle with sides a and b and an included angle of C is:

Area = (1/2)ab*sin(C).

We have a and b, so we want to find C.

Using the Law of Sines, find A:

sin(A)/a = sin(B)/b

==> sin(A)/2 = sin(130°)/6

==> sin(A) = sin(130°)/3

==> A = arcsin[sin(130°)/3] ≈ 14.8°.

(Note that B is obtuse, so we don't need to worry about the ambiguous case.)

Since the angles of a triangle add to 180°:

A + B + C = 180° ==> C = 180° - A - B = 180° - 14.8° - 130° = 35.2°.

Therefore, the area of the triangle is:

A = (1/2)ab*sin(C)

= (1/2)(2)(6)sin(35.2°)

≈ 3.46 units^2.

I hope this helps!

#1