A triangles sides are 6cm 10 cm and 12cm what is the triangles area?

Answer 1

First draw the triangle ABC, where opposite the angle A there is a = 6, opposite the angle B there is b = 10, and opposite the angle C there is c = 12.

Use the law of cosine to find the measure of one of the angles. For example find the measure of the angle C.

cos C = (a^2 + b^2 - c^2)/(2ab)

cos C = (6^2 + 10^2 - 12^2)/[(2)(6)(10)

cos C = (36 + 100 - 144)/120

cos C = -8/120

C = arccos (-8/120) (arccos is the inverse cosine function)

C = 94 degrees.

How to find arccos in the calculator:

Put your calculator on degree mode.

Press 2nd, cos, ( - ), 8 , division symbol, 120, ), Enter.

The window will show 93.82255373, since 8 < 5approximate that to 94.

Now, you can find the area using the formula:

Area of triangle ABC = (1/2)(ab)(sin C) Substitute:

A = (1/2)(6)(10)(sin 94) = 30

How to proceed in your calculator:

.5 x 6 x 10 x sin (94) Enter.

The calculator will show 29.92692151, since 9 < 5approximate that to 30.