Question

use the following figure to complete the following sentences. select all that apply
the side with length a is
☐ adjacent to ∠a
☐ adjacent to ∠b
☐ opposite of ∠a
☐ opposite of ∠b
☐ the hypotenuse
you did not select all of the correct options.
the side with length b is
☐ adjacent to ∠a
☐ adjacent to ∠b
☐ opposite of ∠a
☐ opposite of ∠b
☐ the hypotenuse
you did not select all of the correct options.
the side with length c is
options not fully visible
you did not select all of the correct options.

Explanation:

Step1: Analyze side \( a \)

In right triangle \( \triangle ABC \) (right - angled at \( C \)):

• For an angle in a right triangle, the adjacent side is the non - hypotenuse side that forms the angle with the other side, and the opposite side is the side that does not form the angle. The hypotenuse is the side opposite the right angle.
• \( \angle A \): The sides forming \( \angle A \) are \( b \) (adjacent) and \( c \) (hypotenuse), so \( a \) is opposite to \( \angle A \).
• \( \angle B \): The sides forming \( \angle B \) are \( a \) (adjacent) and \( c \) (hypotenuse), so \( a \) is adjacent to \( \angle B \).
• The hypotenuse is \( c \), so \( a \) is not the hypotenuse. So for side \( a \), the correct options are "adjacent to \( \angle B \)" and "opposite of \( \angle A \)".

Step2: Analyze side \( b \)

• \( \angle A \): The sides forming \( \angle A \) are \( b \) (adjacent) and \( c \) (hypotenuse), so \( b \) is adjacent to \( \angle A \).
• \( \angle B \): The sides forming \( \angle B \) are \( a \) (adjacent) and \( c \) (hypotenuse), so \( b \) is opposite to \( \angle B \).
• The hypotenuse is \( c \), so \( b \) is not the hypotenuse. So for side \( b \), the correct options are "adjacent to \( \angle A \)" and "opposite of \( \angle B \)".

Step3: Analyze side \( c \)

• In a right triangle, the hypotenuse is the side opposite the right angle ( \( \angle C \) here). Also, for \( \angle A \), \( c \) is the hypotenuse (opposite the right angle) and for \( \angle B \), \( c \) is also the hypotenuse. So \( c \) is the hypotenuse, and it is opposite to the right angle \( \angle C \).

Answer:

s:

For "The side with length \( a \) is":

• adjacent to \( \angle B \)
• opposite of \( \angle A \)

For "The side with length \( b \) is":

• adjacent to \( \angle A \)
• opposite of \( \angle B \)

For "The side with length \( c \) is":

• the hypotenuse