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直角三角形
如何把 $\cos(\theta)$ 与 $\sin(\theta)$ 看作斜边为 $1$ 的直角三角形中的边长？
1. Introduction
Introduction
2. The geometry of triangles
The geometry of triangles
3. Ratios of sides in right triangles
Ratios of sides in right triangles
4. Using a ratio involving sine and cosine
Using a ratio involving sine and cosine
5. Summary
Summary
6. Missing leg from the hypotenuse
A right triangle has hypotenuse 1 and one leg 3/5. What is the other leg, as an exact fraction?
7. Why the two triangles are similar
Two nested right triangles share an acute angle at the origin. Why are they similar, and what follows for their side ratios?
8. Coordinates on a circle of radius r
A point at angle theta on a circle of radius r has x = r cos(theta) and y = r sin(theta). What is y when r = 7 and theta = pi/6? Give the exact value.
9. Solving a right triangle from an angle and side
A right triangle has hypotenuse 7 and one acute angle pi/7. What are the two legs, approximately?
10. Two angles from two sightings
A right triangle has hypotenuse 13 and one leg 6.5. What are its acute angles?
11. Shadow and streetlight height
A person 50 feet from a streetlight casts a 14-foot shadow, and the light ray to the shadow's tip makes 27.5 degrees with the ground. Which relation gives the streetlight's height?
12. Similar triangles have proportional sides
If two right triangles share one acute angle, every pair of corresponding sides is in the same ratio.