Robbie is standing 47 feet from the foot of a tree. The angle elevation of the top of the tree is 35° find the height of the tree.

To find the height of the tree, we can use basic trigonometry. Specifically, we'll use the tangent function, which relates the angle of elevation to the opposite side (height of the tree) and the adjacent side (distance from the tree).

The formula is:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Here:
- \(\theta = 35^\circ\) (the angle of elevation),
- The adjacent side = 47 feet (distance from the foot of the tree),
- The opposite side is the height of the tree (which we need to find).

We can rearrange the formula to solve for the height of the tree:
\[
\text{height} = \tan(\theta) \times \text{adjacent}
\]

Now, let's calculate the height.

\[
\text{height} = \tan(35^\circ) \times 47
\]

Let me calculate that for you.The height of the tree is approximately 32.91 feet.

Do you have any further questions or would you like more details?

Here are 5 related questions for practice:
1. What is the length of the hypotenuse in this scenario?
2. How would the height change if Robbie stood 60 feet away from the tree?
3. What if the angle of elevation were 45° instead? How would the height differ?
4. Can you calculate the angle of elevation if the tree's height were 50 feet?
5. If Robbie moves 20 feet closer to the tree, what would the new angle of elevation be?

**Tip:** Always make sure your calculator is set to the correct mode (degrees or radians) when working with trigonometric functions!

Robbie is standing 47 feet from the foot of a tree. The angle elevation of the top of the tree is 35°. Find the height of the tree.

Discover how to find the height of a tree using trigonometry when the angle of elevation is 35° and the distance from the tree is 47 feet. This step-by-step guide covers key trigonometric concepts like the tangent function, making it ideal for students in Grades 8-10.

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