Question

In right triangle, ABC, b^2 +c^2=34and bc=15.what is the approximate length of side a?

Answer 1

We have a right triangle of which we know:

`b^2+c^2=34`

and

`b\cdot c=15`

We have to find the length of side a.

We can use the Law of cosines and write:

`a^2=b^2+c^2-2bc\cdot\cos (A)`

We can replace with the known values and calculate "a" as:

`\begin{gathered} a^2=(b^2+c^2)-2bc\cdot\cos (A) \\ a^2=34-2\cdot15\cdot\cos (53\degree) \\ a^2\approx34-30\cdot0.602 \\ a^2\approx34-18 \\ a\approx\sqrt[]{16} \\ a\approx4 \end{gathered}`

Answer: a = 4 units [Option C]