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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2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
Given a right triangle where the length of one leg is and the length of the other leg is , what is the length of the hypotenuse ?
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Verified step by step guidance1
Identify the given sides of the right triangle: one leg is \(x_{s} = 10\) and the other leg is \(x_{y} = 24\).
Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse \(r_{y}\) is equal to the sum of the squares of the legs: \(r_{y}^2 = x_{s}^2 + x_{y}^2\).
Substitute the known values into the Pythagorean theorem: \(r_{y}^2 = 10^2 + 24^2\).
Calculate the squares of the legs (but do not find the final sum): \$10^2 = 100\( and \)24^2 = 576$.
Add these squared values to express \(r_{y}^2\) as \(r_{y}^2 = 100 + 576\), then take the square root of both sides to find \(r_{y} = \sqrt{100 + 576}\).
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