Question

Find the length of side x in simplest radical form with a rational denominatorthe number on the left is 43

Answer 1

58.799 or rounding up to the nearest integer 59 units

1) Since we're dealing with a right triangle, and the hypotenuse is opposite to the right triangle, we can use a Trigonometric Ratio, sine to find that measure:

$\begin{gathered} \sin (47)=\frac{opposite}{\text{hypotenuse}} \\ \sin (47)=\frac{43}{x} \\ 0.7313=\frac{43}{x} \\ 0.7313x=43 \\ x=58.799 \\ x\approx59 \end{gathered}$

2) So the length of the hypotenuse is 58.799 or rounding up to the nearest integer 59 units