In the right triangle shown, the length of is units and the length of is units. What is the length of the hypotenuse ?
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
A right triangle has one leg of length units and a hypotenuse of length units. What is the length of the missing leg? If necessary, round to the nearest tenth.
A
units
B
units
C
units
D
units
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Verified step by step guidance1
Identify the given elements of the right triangle: one leg length is 6 units, and the hypotenuse length is 10 units.
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: \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse.
Assign the known values: let the missing leg be \(x\), so \$6^2 + x^2 = 10^2$.
Rewrite the equation to solve for \(x^2\): \(x^2 = 10^2 - 6^2\).
Calculate \(x\) by taking the square root of both sides: \(x = \sqrt{10^2 - 6^2}\). Then, if necessary, round the result to the nearest tenth.
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