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 the trigonometric ratio

We use $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here $\theta = 63^{\circ}$, the hypotenuse is $17$ and the opposite side to $\theta$ is $x$. So $\sin63^{\circ}=\frac{x}{17}$.

Step2: Solve for $x$

We know that $\sin63^{\circ}\approx0.891$. Then $x = 17\times\sin63^{\circ}$. Substituting the value of $\sin63^{\circ}$, we get $x=17\times0.891 = 15.147\approx15.1$. (There was an error above, we should use $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. $\cos63^{\circ}=\frac{x}{17}$, $\cos63^{\circ}\approx0.454$, so $x = 17\times0.454=7.718\approx7.7$)

Answer:

$7.7$