Multiple Choice
Given a circle with a circumference of , what is the radius of the circle?
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2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
Point P is the center of the circle in the figure above. If triangle is a right triangle with right angle at , and , , what is the value of if ?
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Verified step by step guidance1
Identify the given information: triangle \( A P B \) is a right triangle with the right angle at \( A \), and the lengths \( A P = 5 \) and \( P B = 13 \). We need to find \( A B = x \).
Recall the Pythagorean theorem for a right triangle, which states that the square of the hypotenuse equals the sum of the squares of the other two sides. Since the right angle is at \( A \), the side opposite this angle, \( P B \), is the hypotenuse.
Set up the Pythagorean theorem equation: \( (A P)^2 + (A B)^2 = (P B)^2 \). Substitute the known values: \( 5^2 + x^2 = 13^2 \).
Simplify the squares: \( 25 + x^2 = 169 \).
Solve for \( x^2 \) by subtracting 25 from both sides: \( x^2 = 169 - 25 \), then take the square root of both sides to find \( x \).
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