Question

A stick 2 m long is placed vertically at point B. The top of the stick is in line with the top of a tree as seen from point A, which is 3 m from the stick and 30 m from the tree. How tall is the tree?

Answer 1

To solve this question, we will use the concept of similar triangles. Here are the steps to find the height of the tree:

1. **Identify Similar Triangles:**
We have two triangles:
- A smaller triangle formed by the stick, where the height is 2 meters and the distance from the point A is 3 meters.
- A larger triangle formed by the tree, where the height is unknown (let's call this height "h") and the distance from point A is 30 meters.

These two triangles are similar because they both are right-angled triangles and the angles at point A are the same for both triangles. Since the triangles are similar, the ratios of their corresponding sides are equal.

2. **Set Up the Proportion:**
The corresponding sides are the heights of the stick and the tree and the distances from point A. This gives us the proportion:
\[ \frac{\text{Height of stick (2 m)}}{\text{Distance from stick to A (3 m)}} = \frac{\text{Height of tree (h)}}{\text{Distance from tree to A (30 m)}} \]

Which is to say:
\[ \frac{2}{3} = \frac{h}{30} \]

3. **Solve for the Height of the Tree:**
Now, we solve for "h" by cross-multiplying to get:
\[ 2 \times 30 = h \times 3 \]

Which simplifies to:
\[ 60 = 3h \]

Now we divide both sides by 3 to solve for "h":
\[ \frac{60}{3} = h \]

Which results in:
\[ h = 20 \]

So, the height of the tree is 20 meters.

Answer 2

Answer: 20 meters.

Explanation:

1. Keeping on mind the information shown in the figure attached and the similarity of both triangles, you can calculate the height of the tree (h) as you can see below:

`(3)/(30)=(2)/(h)`

2. Now, you must solve for the height. So, you obtain the following result:

`h=(30*2)/(3)\\h=20`

3. Therefore, the height of the tree is 20 meters.