How to Find a Missing Side with Cosine

Step-by-step solution

1. Choose the cosine ratio.

   $$\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$$

   Why: The known angle and hypotenuse both belong to CAH.

2. Substitute the values.

   $$\cos 60^\circ = \frac{a}{12}$$

   Why: The adjacent side is the unknown.

3. Multiply both sides by 12.

   $$a = 12 \times \frac{1}{2} = 6$$

   Why: Multiplying isolates the adjacent side, and cos 60 degrees is 1/2.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\text{hyp} = 10,\quad \theta = 60^\circ$

   Show answer

   $5$

2. 2

   $\text{hyp} = 8,\quad \theta = 45^\circ$

   Show answer

   $4\sqrt{2}$

3. 3

   $\text{hyp} = 20,\quad \theta = 30^\circ$

   Show answer

   $10\sqrt{3}$

4. 4

   $\text{hyp} = 6,\quad \theta = 60^\circ$

   Show answer

   $3$

5. 5

   $\text{hyp} = 14,\quad \theta = 45^\circ$

   Show answer

   $7\sqrt{2}$