Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
calculate the value for x.
answer (round to nearest degree): x = □

Explanation:

Step1: Identify trigonometric ratio

We use tangent since $\tan(x)=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\tan(x)=\frac{2}{3}$.

Step2: Solve for x

$x = \arctan(\frac{2}{3})$. Using a calculator, $x=\arctan(\frac{2}{3})\approx 33.69^{\circ}$. Rounding to the nearest degree gives $x = 34^{\circ}$. However, if we consider the other non - right angle in the triangle, we know that the two non - right angles in a right triangle are complementary. Let the angle we first found be $\alpha$ and the other non - right angle be $x$. So $x = 90^{\circ}-\alpha$. Since $\alpha\approx 34^{\circ}$, then $x\approx 90 - 34=42^{\circ}$.

Answer:

$42$