right triangle trigonometry - sohcahtoa\nright triangle trigonometry relates the sides of a right triangle…

right triangle trigonometry - sohcahtoa\nright triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.\nfill in the missing information. text should be lower case.\ncalculate the value for x.\nanswer (round to 1 decimal): x = (ie 1.2 or 16.0)

right triangle trigonometry - sohcahtoa\nright triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.\nfill in the missing information. text should be lower case.\ncalculate the value for x.\nanswer (round to 1 decimal): x = (ie 1.2 or 16.0)

Answer

Explanation:

Step1: Identify the angle for sine

In right - triangle trigonometry, we use the given acute angle. Here the angle is $38^{\circ}$, so we have $\sin38^{\circ}$.

Step2: Recall the sine ratio

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. The side opposite the $38^{\circ}$ angle is $x$ and the hypotenuse is 15. So $\sin38^{\circ}=\frac{x}{15}$.

Step3: Solve for $x$

We can rewrite the equation as $x = 15\times\sin38^{\circ}$. Since $\sin38^{\circ}\approx0.6157$, then $x=15\times0.6157 = 9.2355$. Rounding to 1 decimal place, $x\approx9.2$.

Answer:

$x = 9.2$