A man 1.8 metre tall observes the angle of elevation of a tree to be 20 degrees, if he is standing 16 metres from the tree. Find the height of the tree.
(h-1.8)/16 = tan 20°
A man 1.8metres tall observes the angle of elevation of a tree to be 26°.if he is standing 16 metres from the tree,find the height of the tree to two decimal places
To find the height of the tree, we can use trigonometry.
Let's represent the height of the tree as 'h' meters.
From the given information, we know:
- the observer's height is 1.8 meters
- the angle of elevation is 20 degrees
- the distance between the observer and the tree is 16 meters
We can use the tangent function to solve for the height of the tree.
tangent(theta) = opposite/adjacent
In this scenario, the opposite side is the height of the tree and the adjacent side is the distance between the observer and the tree.
So, we have:
tan(20) = h/16
To find 'h', we can rearrange the equation:
h = tan(20) * 16
Now, let's calculate the value of 'h':
h = tan(20) * 16
≈ 0.364 * 16
≈ 5.824
Therefore, the height of the tree is approximately 5.824 meters.
To find the height of the tree, we need to use trigonometry, specifically the tangent function. Here's how to do it:
Step 1: Draw a diagram.
Start by drawing a triangle representing the situation. Label one side as the height of the tree (let's call it h), another side as the distance between the man and the tree (16 meters), and the angle of elevation as 20 degrees.
Step 2: Identify the relevant trigonometric ratio.
We need to find the height of the tree, which corresponds to the opposite side of the angle of elevation. So, we will use the tangent function, which is defined as the ratio of the opposite side to the adjacent side.
Step 3: Apply the tangent function.
The tangent of the angle of elevation can be written as:
tan(20 degrees) = h/16
Step 4: Solve for the height of the tree.
To isolate h, multiply both sides of the equation by 16:
16 * tan(20 degrees) = h
Step 5: Calculate the height of the tree.
Use a calculator to find the tangent of 20 degrees, then multiply the result by 16 to get the height of the tree.
If you follow these steps, you should be able to determine the height of the tree.