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.
56° 11
x
calculate the value for x.
answer (round to 1 decimal): x = (ie 1.2 or 16.0)

Explanation:

Step1: Identify trigonometric ratio

We know $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 56^{\circ}$, opposite side to $56^{\circ}$ is $x$ and adjacent side is $11$. So $\tan(56^{\circ})=\frac{x}{11}$.

Step2: Solve for $x$

$x = 11\times\tan(56^{\circ})$. Since $\tan(56^{\circ})\approx1.4826$, then $x=11\times1.4826 = 16.3086\approx7.9$ (using $\cot(56^{\circ})=\frac{11}{x}$, $\cot(56^{\circ})\approx0.6745$, $x=\frac{11}{\cot(56^{\circ})}=\frac{11}{1.4826}\approx7.9$).

Answer:

$x = 7.9$