what is the value of opposite side if tan theta is 60 and adjacant side is 12

The formula for the tangent of an angle \(\theta\) in a right triangle is given by:

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

Given:
\[
\tan(\theta) = 60, \quad \text{adjacent} = 12
\]

Let the opposite side be \(x\). Using the formula:

\[
60 = \frac{x}{12}
\]

Solving for \(x\):

\[
x = 60 \times 12 = 720
\]

So, the value of the opposite side is \(720\) units.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How can you calculate the hypotenuse of the triangle given these values?
2. What is the value of \(\theta\) when \(\tan(\theta) = 60\)?
3. How do the sine and cosine functions relate to the opposite and adjacent sides?
4. What are some practical applications of trigonometry in real life?
5. How would the opposite side change if \(\tan(\theta)\) was a smaller value?

**Tip**: Memorizing basic trigonometric identities can make solving these problems much faster!

What is the value of opposite side if tan theta is 60 and adjacent side is 12?

Find the value of the opposite side in a right triangle where tan(θ) = 60 and the adjacent side is 12 units. This problem uses basic trigonometric principles, including the tangent function formula. Suitable for students in Grades 9-10.

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