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 1 decimal): x = (ie 1.2 or 16.0)

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$, the opposite side to the $30^{\circ}$ angle is $20$ and the hypotenuse is $x$. So, $\sin30^{\circ}=\frac{20}{x}$.

Step2: Recall the value of $\sin30^{\circ}$

We know that $\sin30^{\circ}=\frac{1}{2}$. So, the equation becomes $\frac{1}{2}=\frac{20}{x}$.

Step3: Solve for $x$

Cross - multiply: $x\times1 = 2\times20$. So, $x = 40$. Rounding to 1 decimal place gives $x = 40.0$.

Answer:

$40.0$