Question

Can you help me with number 13? Thank you I am having trouble with it.

Answer 1

In triangle ABC, a is the length of the side opposite to angle A (side BC), b is the length of the side opposite to angle B (side AC), and c is the length of the side opposite to angle C (side AB)

We can use the cosine rule to find the length of each side

`\begin{gathered} a=\sqrt[]{b^2+c^2-2bc\cos A} \\ b=\sqrt[]{a^2+c^2-2ac\cos B} \\ c=\sqrt[]{a^2+b^2-2ab\cos C} \end{gathered}`

From the given figure we can see triangle ABC, where We will use the cosine rule to find c

`c=\sqrt[]{a^2+b^2-2ab\cos 90^(\circ)}`

Since cos(90) = 0, then

`\begin{gathered} c=\sqrt[]{a^2+b^2-2ab(0)} \\ c=\sqrt[]{a^2+b^2-0} \\ c=\sqrt[]{a^2+b^2} \end{gathered}`

The expression equivalent to c is

`\sqrt[]{a^2+b^2}`