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

Explanation:

Step1: Identify the trigonometric ratio

We know the angle $56^{\circ}$ and the side adjacent to it is 11 and we want to find the opposite side $x$. So we use the tangent ratio $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So $\tan56^{\circ}=\frac{x}{11}$.

Step2: Solve for $x$

We know that $\tan56^{\circ}\approx1.4826$. From $\tan56^{\circ}=\frac{x}{11}$, we can solve for $x$ by multiplying both sides by 11. So $x = 11\times\tan56^{\circ}\approx11\times1.4826 = 16.3086\approx16.3$.

Answer:

1. $\tan56^{\circ}=\frac{x}{11}$
2. $x = 16.3$