A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30°with it. The distance between the foot of the tree to the point where the top touches the ground is 8m.Find the height of the tree. Related: 01 - How to measure height of a tall object using Clinometer - Class 10 - Maths?

Question

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30°with it. The distance between the foot of the tree to the point where the top touches the ground is 8m.Find the height of the tree. Related:  01 - How to measure height of a tall object using Clinometer - Class 10 - Maths?

Answer

Answer

Answer

Answer

To find the height of the tree, we can use the concept of trigonometry and the given angle and distance measurements. Let's break down the problem step by step:

1. Understanding the Problem:
- A tree has broken due to a storm, and the broken part is bent so that the top of the tree touches the ground, forming a 30° angle with it.
- We are given that the distance between the foot of the tree and the point where the top touches the ground is 8 meters.
- Our task is to find the height of the tree.

2. Visualizing the Situation:
- Imagine a right-angled triangle formed by the broken part of the tree, the ground, and the line connecting the foot of the tree to the point where the top touches the ground.
- The height of the tree is the length of the side opposite to the 30° angle.

3. Applying Trigonometry:
- In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite to that angle to the length of the hypotenuse.
- In our case, the sine of the 30° angle can be calculated as the height of the tree divided by the distance between the foot and the point where the top touches the ground.
- So, we have sin(30°) = height of tree / 8m.

4. Solving the Equation:
- We can rearrange the equation to isolate the height of the tree:
height of tree = sin(30°) * 8m.
- Now, we substitute the value of sin(30°) with its actual value, which is 0.5:
height of tree = 0.5 * 8m.
- Solving the equation, we find:
height of tree = 4m.

5. Answer:
- The height of the tree is 4 meters.

Using a Clinometer to Measure the Height of a Tall Object:
- A clinometer is a device used to measure the angle of elevation or depression of an object.
- To measure the height of a tall object, such as a tree, using a clinometer, follow these steps:
1. Stand at a known distance from the base of the object, preferably far enough to have a clear view of the top.
2. Hold the clinometer in a way that allows you to look through the sighting tube or lens.
3. Align the clinometer so that the bottom edge is parallel to the ground and the top edge is aligned with the top of the object.
4. Look through the sighting tube or lens and read the angle indicated on the scale.
5. Measure the distance between yourself and the base of the object using a measuring tape or by pacing the distance.
6. Apply trigonometry by using the tangent function to calculate the height of the object:
height of object = distance to the object * tan(angle).

Remember, when using a clinometer, it is important to ensure accuracy by standing on level ground, holding the clinometer steady, and taking multiple measurements for more precision.

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