Warm Up Solve ΔSJT given s = 49, side j = 16, and side T = 115°. S = _____ J = _____ T = _____ s = _____ j = _____ t = _____

Answer Solve ΔSJT given s = 49, side j = 16, and side T = 115°. S = 50.43° J = 14.58° T = 115° s = 48 j = 16 t = 57.62

Area of non-right Triangles

Area of a Triangle A = ½ b h So far, you know the formula to find the area of a triangle is A = ½ b h ….but what if you do not know the height?

AreaΔ= ½ bc sin A = ½ ac sin B = ½ ab sin C We use these formulas! AreaΔ= ½ bc sin A = ½ ac sin B = ½ ab sin C

Example 1 Find the area

Example 2 Farmer Jones owns a triangular piece of land. He labels each corner of the land A, B and C. The length of the AB is 150 m. The length of the fence BC is 231 m. The angle between fence AB and fence BC is 123º. What is the area of the land Farmer Jones owns?

Example 3 Find the area

There is also an area formula that can be used when only the three sides of a triangle are known. Heron’s Formula Let a, b, and c be the sides of ΔABC, and s is the semi- perimeter. Then the area of ΔABC is given by Area =

Example 4 Find the area of a triangle with sides 13, 15, 18.

Example 5 Find the area of the triangle.