Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Height of a Tower The angle of depression from a television tower to a point on the ground 36.0 m from the bottom of the tower is 29.5°. Find the height of the tower.
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 a hypotenuse of length units and one leg of length units. What is the length of the other leg of the triangle?
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: the hypotenuse length \(c = 10\) units and one leg length \(a = 6\) units.
Recall the Pythagorean theorem, which relates the sides of a right triangle: \(a^2 + b^2 = c^2\), where \(b\) is the length of the other leg.
Substitute the known values into the Pythagorean theorem: \$6^2 + b^2 = 10^2$.
Calculate the squares of the known sides: \$36 + b^2 = 100$.
Isolate \(b^2\) by subtracting 36 from both sides: \(b^2 = 100 - 36\), then find \(b\) by taking the square root: \(b = \sqrt{64}\).
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