Math  /  Trigonometry

QuestionFind the measure of xx. x=x= \square

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. One leg of the triangle measures 12 12 .
3. The angle adjacent to this leg is 52 52^\circ .
4. We need to find the hypotenuse x x .

STEP 2

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

STEP 3

Identify the trigonometric function to use:
Since we have the adjacent side and need to find the hypotenuse, we use the cosine function.

STEP 4

Set up the equation using the cosine function:
cos(52)=AdjacentHypotenuse=12x \cos(52^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{12}{x}

STEP 5

Solve for x x :
Rearrange the equation to solve for x x :
x=12cos(52) x = \frac{12}{\cos(52^\circ)}
Calculate x x using a calculator:
x120.6157 x \approx \frac{12}{0.6157} x19.49 x \approx 19.49

STEP 6

Round the solution to the nearest hundredth:
The measure of x x is:
19.49 \boxed{19.49}

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