Multiple Choice
Given a right triangle with one acute angle measuring , how many distinct triangles (up to similarity) can be formed?
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2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
A right triangle has a hypotenuse of units and one leg of units. What is the length of the other leg?
A
units
B
units
C
units
D
units
Verified step by step guidance1
Identify the sides of the right triangle: the hypotenuse \(c = 14\) units, one leg \(a = 7\) units, and the unknown leg \(b\).
Recall the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse: \(a^2 + b^2 = c^2\).
Substitute the known values into the Pythagorean theorem: \$7^2 + b^2 = 14^2$.
Calculate the squares of the known sides: \$49 + b^2 = 196$.
Isolate \(b^2\) by subtracting 49 from both sides: \(b^2 = 196 - 49\), then express \(b\) as \(b = \sqrt{196 - 49}\) to find the length of the other leg.
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