Textbook Question
Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46.
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2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
Given right triangle xyz, if angle x is and the length of the side opposite angle x is , what is the length of the hypotenuse?
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Verified step by step guidance1
Identify the given information: angle \( x = 30^\circ \) and the length of the side opposite angle \( x \) is 5.
Recall the definition of sine in a right triangle: \( \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} \). Here, \( \theta = 30^\circ \).
Set up the equation using sine: \( \sin(30^\circ) = \frac{5}{\text{hypotenuse}} \).
Solve for the hypotenuse by multiplying both sides by the hypotenuse and then dividing both sides by \( \sin(30^\circ) \): \( \text{hypotenuse} = \frac{5}{\sin(30^\circ)} \).
Use the known value or a calculator to find \( \sin(30^\circ) \) if needed, but do not calculate the final numeric value unless asked.
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