Concept 8.4
From One Ratio to All the Others
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
If one trigonometric ratio of an acute angle is known, the others can be found by drawing a right triangle with those sides and using Pythagoras to find the third side.
The intuition
sin A = 3/5 means the opposite side and the hypotenuse are in the ratio 3 : 5. Draw them as 3 and 5.
Pythagoras gives the missing side: √(5² − 3²) = 4. Now every ratio is a reading: cos A = 4/5, tan A = 3/4.
The attention
Look for the missing side first. Every other ratio is read from it.
sin A = 3/5: opposite 3, hypotenuse 5, adjacent = 4 ⇒ cos A = 4/5 not 3/5
Look hereNot here
- Look here
- The missing side, found by Pythagoras. Only the third side is new information. Once you have it, cos A and tan A are just readings.
- Not here
- Reusing the numbers you were given. Reusing 3 and 5 in another ratio gives sin A again. cos A needs the adjacent side, which you haven't been told.
- What it teaches
- Before computing, ask what is missing. Find that one thing first.