Given an angle \theta (pronounced "th-ay-ta") in a right triangle, the sides of the triangle have some special names: opposite, adjacent and hypotenuse.

  • Opposite: the side opposite to the angle \theta.

  • Adjacent: the side next to (or touching) the angle \theta.

  • Hypotenuse: the longest side of the triangle, which is always opposite to the right angle.

The opposite and adjacent sides are relative to the angle in question. If \theta is representing the other angle, then the name of these sides change to reflect their position relative to the other angle.

Note that the variable \theta is the most commonly used variable in trigonometry, just like x in algebra. However, other variables are often used as well.

FLAG

Relative to \angle L , which sides are the opposite, adjacent, and hypotenuse?

EXPLANATION

Relative to \angle L,

  • the opposite side is \overline{MK},

  • the adjacent side is \overline{LM}, and

  • the hypotenuse is \overline{LK}.

FLAG

Which of the following statements is true?

a
$\overline{XZ}$ is the side opposite to $\angle X$
b
$\overline{YZ}$ is the side adjacent to $\angle X$
c
$\overline{YZ}$ is the side opposite to $\angle Y$
d
$\overline{XZ}$ is the side adjacent to $\angle Y$
e
$\overline{YZ}$ is the side opposite to $\angle X$

Which of the following statements is true?

a
$\overline{QR}$ is opposite to $\angle Q$
b
$\overline{PR}$ is opposite to $\angle P$
c
$\overline{QR}$ is adjacent to $\angle P$
d
$\overline{QR}$ is adjacent to $\angle Q$
e
$\overline{QR}$ is opposite to $\angle R$

Relative to \angle LMK, what is the length of the adjacent side?

EXPLANATION

The adjacent side to \angle LMK is \overline{MK}, and its length is 12.

FLAG

Relative to $\angle ABC,$ what are the lengths of the opposite, adjacent, and hypotenuse, respectively?

a
$8,\, 17,\, 15$
b
$8,\, 15,\, 17$
c
$15,\, 8,\, 17$
d
$17,\, 8,\, 15$
e
$17,\, 15,\, 8$

Relative to $\angle LMK,$ what are the lengths of the opposite, adjacent, and hypotenuse, respectively?

a
$13,\, 12,\, 5$
b
$5,\, 13,\, 12$
c
$13,\, 5,\, 12$
d
$12,\, 5,\, 13$
e
$12,\, 13,\, 5$

Relative to the angles \theta and \alpha, which sides are the opposite sides?

EXPLANATION

Relative to the angle \theta, the opposite side is \overline{KL}.

Relative to the angle \alpha, the opposite side is \overline{QR}.

FLAG

Which sides are opposite to the angles $\theta$ and $\alpha,$ respectively?

a
$\overline{MN}$ and $\overline{RP}$
b
$\overline{PQ}$ and $\overline{ON}$
c
$\overline{RQ}$ and $\overline{MN}$
d
$\overline{RP}$ and $\overline{MO}$
e
$\overline{MO}$ and $\overline{PQ}$

Which sides are adjacent to the angles $\theta$ and $\alpha$, respectively?

a
$\overline{LM}$ and $\overline{VW}$
b
$\overline{NL}$ and $\overline{UV}$
c
$\overline{MN}$ and $\overline{UV}$
d
$\overline{MN}$ and $\overline{UW}$
e
$\overline{NL}$ and $\overline{UW}$
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