How to Find a Missing Side with Tangent

Step-by-step solution

1. Choose the tangent ratio.

   $$\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$$

   Why: Tangent links the two legs, and the adjacent leg is known.

2. Substitute the values.

   $$\tan 45^\circ = \frac{o}{9}$$

   Why: The opposite side is the unknown.

3. Multiply both sides by 9.

   $$o = 9 \times 1 = 9$$

   Why: tan 45 degrees is 1, so the two legs are equal.

Practice problems

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

1. 1

   $\text{adj} = 5,\quad \theta = 45^\circ$

   Show answer

   $5$

2. 2

   $\text{adj} = 6,\quad \theta = 30^\circ$

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   $2\sqrt{3}$

3. 3

   $\text{adj} = 4,\quad \theta = 60^\circ$

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   $4\sqrt{3}$

4. 4

   $\text{adj} = 10,\quad \theta = 45^\circ$

   Show answer

   $10$

5. 5

   $\text{adj} = 3,\quad \theta = 30^\circ$

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   $\sqrt{3}$