Multiple Choice
Given a right triangle where angles and are acute and is supplementary to , which of the following relationships is false?
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
In the figure above, points and lie on a circle with center . If triangle is a right triangle with right angle at , and , , what is the value of (denoted as )?
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Verified step by step guidance1
Identify the given elements: triangle OPQ is a right triangle with the right angle at P, and the lengths OP = 5 and OQ = 13 are given.
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 P, the side opposite P (OQ) is the hypotenuse.
Set up the Pythagorean theorem equation: \(OQ^2 = OP^2 + PQ^2\), where \(PQ\) is the side we want to find (denoted as \(s\)).
Substitute the known values into the equation: \$13^2 = 5^2 + s^2$.
Solve for \(s^2\) by isolating it: \(s^2 = 13^2 - 5^2\). Then, take the square root of both sides to find \(s\).
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