Multiple Choice
In a right triangle, two interior angles each measure . Which of the following statements is true about this triangle?
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2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
In the right triangle shown, the length of is units and the length of is units. What is the length of the hypotenuse ?
A
units
B
units
C
units
D
units
Verified step by step guidance1
Identify the sides of the right triangle: sides \(a = 6\) units and \(b = 8\) units are the legs, and \(c\) is the hypotenuse, which is the side opposite the right angle.
Recall the Pythagorean theorem, which relates the sides of a right triangle: \(c^2 = a^2 + b^2\). This formula allows us to find the hypotenuse when the legs are known.
Substitute the known values into the Pythagorean theorem: \(c^2 = 6^2 + 8^2\).
Calculate the squares of the legs: \(6^2 = 36\) and \(8^2 = 64\), then add them to get \(c^2 = 36 + 64\).
Take the square root of both sides to solve for \(c\): \(c = \sqrt{36 + 64}\). This will give the length of the hypotenuse.
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