Question

triangle | given side for angle | missing side for angle (x) | correct ratio to use sin, cos, tan
1 | adjacent | | cos
2 | | opposite |
3 | hypotenuse | |
4 | | |

Explanation:

To solve this, we recall the trigonometric ratios:

• $\boldsymbol{\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}}$
• $\boldsymbol{\tan\theta = \frac{\text{opposite}}{\text{adjacent}}}$
• $\boldsymbol{\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}}$

Row 1:

Given: Adjacent side, Ratio = $\cos$.
From $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$, the missing side is hypotenuse.

Row 2:

Missing side: Opposite, Given side (inferred) = Adjacent (since $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$).
Ratio: $\boldsymbol{\tan}$.

Row 3:

Given: Hypotenuse, Missing side = Opposite (from $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$).
Ratio: $\boldsymbol{\sin}$.

Filled Table:

Triangle	Given side for angle	Missing side for angle (x)	Correct ratio to use (sin, cos, tan)
②	adjacent	opposite	tan
③	hypotenuse	opposite	sin

(Note: For a complete table, additional rows can follow the same trigonometric ratio logic.)

Answer:

To solve this, we recall the trigonometric ratios:

• $\boldsymbol{\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}}$
• $\boldsymbol{\tan\theta = \frac{\text{opposite}}{\text{adjacent}}}$
• $\boldsymbol{\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}}$

Row 1:

Given: Adjacent side, Ratio = $\cos$.
From $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$, the missing side is hypotenuse.

Row 2:

Missing side: Opposite, Given side (inferred) = Adjacent (since $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$).
Ratio: $\boldsymbol{\tan}$.

Row 3:

Given: Hypotenuse, Missing side = Opposite (from $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$).
Ratio: $\boldsymbol{\sin}$.

Filled Table:

Triangle	Given side for angle	Missing side for angle (x)	Correct ratio to use (sin, cos, tan)
②	adjacent	opposite	tan
③	hypotenuse	opposite	sin

(Note: For a complete table, additional rows can follow the same trigonometric ratio logic.)