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.
sin□ = \frac{□}{□}
calculate the value for x.
answer (round to 1 decimal): x = □
(ie 1.2 or 16.0)

Explanation:

Step1: Identify sine ratio

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 38^{\circ}$, the opposite side to the $38^{\circ}$ angle is $x$ and the hypotenuse is 15. So, $\sin(38^{\circ})=\frac{x}{15}$.

Step2: Solve for x

We know that $\sin(38^{\circ})\approx0.6157$. Then, from $\sin(38^{\circ})=\frac{x}{15}$, we can solve for $x$ by multiplying both sides by 15. So, $x = 15\times\sin(38^{\circ})=15\times0.6157 = 9.2355\approx9.2$.

Answer:

sin(38°) = $\frac{x}{15}$; x = 9.2