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]