Math / Trigonometry

QuestionFind the measure of $x$ . $x=[?$

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. One angle is $78^\circ$ .
3. The hypotenuse is $26$ .
4. The side opposite the $78^\circ$ angle is labeled as $x$ .

STEP 2

1. Identify the appropriate trigonometric function.
2. Set up the equation using the trigonometric function.
3. Solve for $x$ .
4. Round the solution to the nearest hundredth.

STEP 3

Identify the appropriate trigonometric function. Since we are dealing with a right triangle and need to find the side opposite a given angle, we use the sine function:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

STEP 4

Set up the equation using the sine function for the angle $78^\circ$ :
$\sin(78^\circ) = \frac{x}{26}$

STEP 5

Solve for $x$ by multiplying both sides by $26$ :
$x = 26 \times \sin(78^\circ)$

STEP 6

Calculate the value of $x$ and round to the nearest hundredth. Use a calculator to find $\sin(78^\circ)$ :
$x \approx 26 \times 0.9781$ $x \approx 25.43$
The measure of $x$ is:
$\boxed{25.43}$

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