Question

Find the shaded region if AB is 3cm, AC is 4cm and BC is 5cm.​

Answer 1

Answer:

Step-by-step explanation:

It's called the "Law of cosines" and can be aplied in each and every triangle.

Law of cosines: In the ABC triangle,

\displaystyle BC^{2}=AB^{2}+AC^{2}-2XABXACBC

2

=AB

2

+AC

2

−2XABXAC

Let's consider that our ABC triangle has the measures in the following way:

AB=3; BC=5; AC=4

Applying the Law of cosines:

\displaystyle 5^{2}=3^{2}+4^{2}-2X3X4XcosAcos A=0 => A=90^\circ => sinA=15

2

=3

2

+4

2

−2X3X4XcosAcosA=0=>A=90

∘

=>sinA=1

An area formula is ABXACXsinA / 2.

So, the ABC's area is 3X4X1/2=6