https://file.aiquickdraw.com/mathbot/file/1726018897317soekhhwq.jpg

In this image, we have a right-angled triangle with the following given information:

- One angle is \(72^\circ\).
- The adjacent side (relative to the \(72^\circ\) angle) is 2.3 m.
- We need to find the length of side \(b\), which is the side opposite to the \(72^\circ\) angle.

We can use the **tangent function** to solve for side \(b\). The tangent of an angle in a right triangle is given by:

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

Here:
- \(\theta = 72^\circ\)
- The adjacent side = 2.3 m
- The opposite side = \(b\) (what we're solving for)

Rearranging the formula to solve for \(b\):

\[
b = \text{adjacent} \times \tan(\theta)
\]

Now, let's calculate the value of \(b\).The length of the unknown side \(b\) is approximately **7.08 meters**, rounded to three significant figures.

Would you like a detailed breakdown of the steps or further clarification on any part of this?

Here are 5 related questions to explore further:

1. How can we use the sine or cosine functions to solve for other sides of the triangle?
2. What is the hypotenuse of this triangle, and how can we calculate it?
3. How would the result change if the angle were smaller, say \(60^\circ\)?
4. Can you solve for \(b\) if only the hypotenuse and the angle are given?
5. How does the tangent function relate to the other trigonometric ratios?

**Tip:** Always ensure your calculator is set to degrees when working with angles measured in degrees, especially when using trigonometric functions.

In relation to the right-angle triangle pictured, what is the value of the unknown side b?

Solve for the unknown side of a right-angle triangle using trigonometric functions. Given an angle of 72° and an adjacent side of 2.3 meters, find the length of side b using the tangent function. Perfect for students in Grades 9-11.

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