Class 10 Maths · Chapter 8 · Topic 1 of 5
Name the sides from the chosen angle
Name the sides from the angle you have chosen.
Ideas you’ll use
- Opposite, adjacent and hypotenuse
- The hypotenuse is opposite the right angle. The opposite side faces the chosen acute angle. The adjacent side touches it but is not the hypotenuse.
Understand it, one idea at a time
Choose an idea. Follow its reason, calculation and clue in the picture.
Choose θ before naming the sides
- Opposite
- Across from the chosen acute angle.
- Adjacent
- Touches the angle; exclude the hypotenuse.
- Hypotenuse
- Opposite the right angle and longest side.
Find the right angle
Its opposite side is the hypotenuse, regardless of how the diagram is turned.
hypotenuse=13 in a 5–12–13 triangleIn the picture: Locate the right-angle mark first.
Read all the reasoning together
Find the right angle
Its opposite side is the hypotenuse, regardless of how the diagram is turned.
hypotenuse=13 in a 5–12–13 triangleChoose the acute angle
Looking from the angle opposite 5 makes that side opposite and the other leg adjacent.
opposite=5; adjacent=12Switch viewpoints
For the other acute angle, opposite and adjacent exchange, but the hypotenuse does not.
opposite=12; adjacent=5; hypotenuse=13
Name the sides from the angle you have chosen.
Worked example: Angle choice changes the names
In a 5–12–13 right triangle, choosing the angle opposite 5 makes opposite = 5 and adjacent = 12For the other acute angle, opposite = 12 and adjacent = 5. Both use hypotenuse 13.
Read the supporting explanation
If we switch to the other acute angle, the opposite and adjacent sides exchange roles. The hypotenuse stays the same. A picture may be turned or reflected, so side names do not mean “vertical”, “horizontal” and “sloping”.
Go deeper: First draw the triangle
Label the given lengths, right angle and chosen angle. This avoids guessing a ratio before knowing which sides the problem actually gives.
Your turn
Try the idea yourself. Show your reasoning, then compare.
Question
Does the side touching the angle always mean the adjacent side?
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