Select your answer If the side adjacent to an angle has a length of 4 and the tangent of the angle equals 0.5 , what is the length of the side opposite the angle? 1 4 8

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To find the length of the side opposite the angle, we can use the definition of the tangent function in a right triangle. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Given:
- Length of the adjacent side $$ a = 4 $$
- Tangent of the angle $$ \tan(\theta) = 0.5 $$

The formula for tangent is:

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

Let $$ o $$ be the length of the opposite side. We can set up the equation:

$$
0.5 = \frac{o}{4}
$$

Now, we can solve for $$ o $$:

$$
o = 0.5 \times 4
$$

Calculating this gives:

$$
o = 2
$$

However, the options provided are 1, 4, and 8. Since 2 is not one of the options, let's check the calculations again.

1. We have $$ \tan(\theta) = 0.5 $$.
2. The adjacent side is 4.
3. Therefore, $$ o = 0.5 \times 4 = 2 $$.

Since 2 is not an option, it seems there might be a misunderstanding in the options provided. The correct length of the opposite side is indeed 2 based on the calculations.

If you have any further questions or need clarification, feel free to ask!
The length of the opposite side is 2.

Select your answer If the side adjacent to an angle has a length of 4 and the tangent of the angle equals 0.5 , what is the length of the side opposite the angle? 1 4 8

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