Question

solve for ( x ). round to the nearest tenth, if necessary.
(there is a right triangle ( onm ) with right angle at ( n ), angle at ( m ) is ( 75^circ ), length of ( on ) is ( 6.3 ), length of ( om ) is ( x ))
answer attempt 1 out of 5
( x = ) input box submit answer

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\angle O = 15^\circ$ (since triangle sum is $180^\circ$, $180-90-75=15$), opposite side to $\angle O$ is $x$, hypotenuse is $6.3$.

Step2: Set up the equation

$\sin(15^\circ)=\frac{x}{6.3}$

Step3: Solve for $x$

$x=6.3\times\sin(15^\circ)$
Calculate $\sin(15^\circ)\approx0.2588$, so $x\approx6.3\times0.2588\approx1.6$

Answer:

$1.6$