Question

complete the table to show the name of each side of the right triangle when you consider angles a and b. opposite side opposite side adjacent side adjacent side hypotenuse hypotenuse (right triangle diagram with vertices a, b, c, right angle at c, sides labeled a, b, c) (table with columns a, b, c and rows ∠a, ∠b, empty cells to fill)

Explanation:

Step1: Recall right triangle side definitions

In a right triangle, the hypotenuse is the side opposite the right angle (always the longest side). The opposite side to an angle is the side not forming the angle, and the adjacent side is the side (other than hypotenuse) forming the angle.

For $\angle A$:

• Opposite side: The side opposite $\angle A$ is $a$ (since $\angle A$ is at vertex A, side opposite is BC which is length $a$).
• Adjacent side: The side adjacent to $\angle A$ (other than hypotenuse) is $b$ (side AC, length $b$).
• Hypotenuse: The hypotenuse is $c$ (side AB, opposite right angle at C).

For $\angle B$:

• Opposite side: The side opposite $\angle B$ is $b$ (side AC, length $b$).
• Adjacent side: The side adjacent to $\angle B$ (other than hypotenuse) is $a$ (side BC, length $a$).
• Hypotenuse: The hypotenuse is still $c$ (side AB, as it's opposite right angle at C).

Step2: Fill the table

For $\angle A$ row:

• Column $a$: Opposite Side
• Column $b$: Adjacent Side
• Column $c$: Hypotenuse

For $\angle B$ row:

• Column $a$: Adjacent Side
• Column $b$: Opposite Side
• Column $c$: Hypotenuse

Answer:

	$a$	$b$	$c$
$\angle B$	Adjacent Side	Opposite Side	Hypotenuse