Math / Trigonometry

Question34° X 10 a

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. One angle is $34^\circ$ .
3. The side opposite the $34^\circ$ angle is labeled $x$ .
4. The hypotenuse is labeled $10$ .

STEP 2

1. Identify the trigonometric function that relates the angle, opposite side, and hypotenuse.
2. Set up the equation using the trigonometric function.
3. Solve for $x$ .

STEP 3

Identify the trigonometric function that relates the angle, opposite side, and hypotenuse. In a right triangle, the sine function relates these components:
$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$

STEP 4

Set up the equation using the sine function for the given angle $34^\circ$ :
$\sin(34^\circ) = \frac{x}{10}$

STEP 5

Solve for $x$ by multiplying both sides by $10$ :
$x = 10 \times \sin(34^\circ)$
Calculate the value of $x$ :
$x \approx 10 \times 0.5592$ (using $\sin(34^\circ) \approx 0.5592$ )
$x \approx 5.592$
The length of the side opposite the $34^\circ$ angle is approximately:
$\boxed{5.592}$

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