Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
fill in the missing information. text should be lower case.
12
16°
calculate the value for x.
answer (round to 1 decimal): x =
(ie 1.2 or 16.0)

Explanation:

Step1: Identify the trig - ratio

We know the adjacent side to the $16^{\circ}$ angle is $12$ and we want to find the opposite side $x$. We use the tangent ratio $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan\theta=\frac{x}{12}$

Step2: Substitute the angle value

Since $\theta = 16^{\circ}$, we have $\tan(16^{\circ})=\frac{x}{12}$.

Step3: Solve for $x$

We know that $\tan(16^{\circ})\approx0.2867$, so $x = 12\times\tan(16^{\circ})$.
$x=12\times0.2867 = 3.4404\approx4.3$ (rounded to 1 decimal place)

Answer:

$x = 4.3$