Certainly! Here's a practical example where you would use the tangent ratio in grade 10 trigonometry:

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Example: Finding the Height of a Tree

Imagine you're standing 30 meters away from a tree. You want to find the height of the tree, but you can't measure it directly. Instead, you measure the angle of elevation from your eyes to the top of the tree, which is 35°.

To find the height of the tree, we can use the tangent ratio, since the tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the tree).

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Step-by-step solution:

1. Set up the situation:

   • Angle of elevation = 35°
   • Distance from the tree (adjacent side) = 30 meters
   • Height of the tree (opposite side) = ? (this is what we want to find)

2. Write the tangent ratio formula:

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

   Where:

   • $\theta = 35^\circ$
   • Opposite = height of the tree (we'll call it $h$)
   • Adjacent = 30 meters

   So the equation becomes:

   $\tan(35^\circ) = \frac{h}{30}$

3. Solve for the height of the tree (h):

   $h = 30 \times \tan(35^\circ)$

   Using a calculator:

   $h \approx 30 \times 0.7002$

   $h \approx 21.01 \, \text{meters}$

So, the height of the tree is approximately 21.01 meters.

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This is a real-life application of the tangent ratio, which helps you find unknown heights or distances when you know the angle of elevation and the adjacent side in a right triangle.

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Would you like to see more examples or details on this topic?

Related Questions:

1. How can you use tangent to find the height of a building from a certain distance?
2. What is the difference between using tangent and sine for such problems?
3. How do you solve for an unknown angle using the tangent ratio?
4. Can tangent be used in any right triangle, or is it limited to certain types?
5. What are the other primary trigonometric ratios, and how do they compare to tangent?

Tip: Always make sure your calculator is set to the correct mode (degrees or radians) depending on the units you're using for the angle!