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Why do similar triangles have the same trigonometric ratios?
Trigonometric ratios are characteristics of angles, not of lengths. And, by definition, the corresponding angles an similar triangles have the same measures.
What are trig ratios?
Trig ratios or to give them their proper name are trigonometrical rations applicable to right angle triangles and they are tangent ratio, sine ratio and cosine ratio.
determine the speed of rotation of a 20 tooth gear when it is driven by a 40 tooth gear and rotating at 10 rpm?
To determine the speed of rotation of a gear driven by another gear, you can use the gear ratio formula: Gear Ratio = Number of Teeth on Driven Gear / Number of Teeth on Driving Gear. In this case, the gear ratio is 40/20 = 2. Since the driving gear is rotating at 10 rpm, the driven gear will rotate at 10 rpm / 2 = 5 rpm.
Can trig ratios only be used on right triangles?
Yes
How was trigonometry discovered?
Ancient Egyptian and Babylonian mathematicians lacked the concept of an angle measure, but they studied the ratios of the sides of similar triangles and discovered some properties of these ratios. The ancient Nubians used a similar methodology.
