Which side faces the angle?

The idea

In a right triangle, the side facing an acute angle A is the side opposite to angle A, and the side other than the hypotenuse that forms part of angle A is the side adjacent to angle A.

The Minar and the student

A student stands on the ground and looks up at the top of the Qutub Minar. The ground, the Minar and the line of sight make a right triangle.

The angle at the student's feet is between the ground and the line of sight. The Minar stands straight up from the ground, so the angle at its foot is a right angle.

Which side of this triangle is across from the angle at the student?

• The Minar
• The ground
• The line of sight

Tap the side

Each picture marks one angle in purple. Tap the side that is asked for. Watch what happens when the marked angle changes to C.

The names depend on the angle

In a right triangle, the side facing an acute angle A is the side opposite to angle A. The side other than the hypotenuse that is part of angle A is the side adjacent to angle A. The hypotenuse is across from the right angle.

In triangle ABC, right-angled at B: for angle A, BC is opposite and AB is adjacent. For angle C they swap: AB is opposite and BC is adjacent. Only the hypotenuse AC keeps its name.

Notes

Opposite to angle A: the side that faces A. Adjacent to angle A: the side, other than the hypotenuse, that is part of A. The hypotenuse faces the right angle. Change the angle and the opposite and adjacent sides swap.

Check yourself

The student at point A looks up at the top C of the Minar, and B is the foot of the Minar. Which side is adjacent to the angle at A?

In the picture, which side is opposite to angle R?

In triangle ABC, right-angled at B, the side BC is opposite to angle A. What is BC for angle C?

A right triangle has sides of 6 cm, 8 cm and 10 cm. How long is its hypotenuse (in cm)?

Answer: 10

The hypotenuse is the longest side of a right triangle, so it is 10 cm.

• BC, the Minar. The Minar is across from the angle at A. It is the opposite side, not the adjacent one.
• AB, the ground — correct. Yes! The ground AB is a side of the angle at A, next to it. The other side of the angle is the line of sight, which is the hypotenuse.
• AC, the line of sight. The line of sight is across from the right angle at the foot of the Minar. It is the hypotenuse.
• PQ — correct. Yes! PQ does not touch R. It faces the angle R.
• QR. QR is a side of angle R. It touches the angle, so it is the adjacent side.
• PR. PR is across from the right angle at Q. It is the hypotenuse.
• Opposite to C. BC is a side of angle C, so it touches the angle. It is not opposite to C.
• Adjacent to C — correct. Yes! BC is a side of angle C, next to it. The names swap when the angle changes.
• The hypotenuse. The hypotenuse is AC, across from the right angle at B. It does not change with the angle.