A triangular plot of land has sides that measure 5 meters 7 meters and 10 meters What is the area of this plot of land to the nearest tenth of a square meter?

This is NOT a Pythagorean triangle.

So we must fall back on the Cosine Rule for an agular value.

Cosine Rule is a^(2) = b^(2) + c^(2) - 2bcCosA

Algebraically rearranging

CosA = [a^(2) - b^(2) - c^(2)] / -2bc

Substituting

CosA = [10^(2) - 7^(2) - 5^)2)] / -(2(7)(5))

CosA = [100 - 49 - 25]/-70

CosA = 26/-70

CosA = -0.371428571...

A = Cos^(-1) -0.371428573

A =111.8037 481 ... degrees. -

Now area of triangle is 0.5 X Base X height

The height is = 7Sin(111.8037481...)

Hence are is 0.5(5)(7)Sin(111.8037481...)

Area = 16.248... m^(2)