Question

julian describes an angle in the triangle using these statements.
(overline{gh}) is the adjacent side.
(overline{hk}) is the opposite side.
(overline{gk}) is the hypotenuse.
which angle(s) is julian describing?
(angle g)
(angle h)
(angle k)
(angle h) and (angle k)

Explanation:

Step1: Recall the definitions of adjacent, opposite sides and hypotenuse in a right - triangle

In a right - triangle, for a given non - right angle:

• The adjacent side is the side that forms the angle (other than the hypotenuse).
• The opposite side is the side that does not form the angle and is across from the angle.
• The hypotenuse is the longest side of the right - triangle (opposite the right angle).

Step2: Analyze for $\angle G$

• For $\angle G$, $\overline{GH}$ is one of the sides forming $\angle G$ (so it is the adjacent side).
• $\overline{HK}$ is across from $\angle G$ (so it is the opposite side).
• $\overline{GK}$ is the hypotenuse (longest side of the right - triangle $\triangle GHK$ with right angle at $H$).

Step3: Analyze for $\angle H$

$\angle H$ is a right angle. The concepts of opposite and adjacent sides (in the context of trigonometric ratios for non - right angles) do not apply in the same way.

Step4: Analyze for $\angle K$

• For $\angle K$, the adjacent side would be $\overline{HK}$ and the opposite side would be $\overline{GH}$. But Julian said $\overline{GH}$ is the adjacent side and $\overline{HK}$ is the opposite side.

So, Julian is describing $\angle G$.

Answer:

$\angle G$