A man 1.7m tall observes a bird on the top of a tree at an angle of 30degree. If the distance between the man's head the bird is 25m, what is the height of the tree?
(h-1.7)/25 = sin30°
h1 = 1.7 m.
sin30 = h2/25
h2 = 25*sin30 = 12.5 m.
h1+h2 = 1.7+12.5 = ___ m. = Ht. of tree.
To find the height of the tree, we can use trigonometry. Let's call the height of the tree "h."
1. We have a right triangle formed by the man, the bird, and the height of the tree. The angle between the man's line of sight and the height of the tree is 30 degrees.
2. The opposite side of the right angle triangle is the height of the tree (h).
3. The adjacent side of the triangle is the distance between the man's head and the bird, which is 25 meters.
4. We have the opposite side and the adjacent side, so we can use the tangent function to find the height of the tree.
tan(30 degrees) = h / 25
5. Rearranging the equation, we can solve for h:
h = 25 * tan(30 degrees)
6. Now, let's calculate the value of tan(30 degrees) and find the height of the tree:
tan(30 degrees) ≈ 0.5774
h ≈ 25 * 0.5774
h ≈ 14.435 meters
Therefore, the height of the tree is approximately 14.435 meters.
To find the height of the tree, we can use trigonometry. Let's break down the problem step-by-step:
Step 1: Draw a diagram representing the situation.
Start by drawing a straight line to represent the height of the tree. Label the bottom of the line as the man's position and the top of the line as the position of the bird.
Step 2: Identify the given information.
We are given the following information:
- The man's height is 1.7m.
- The angle between the man's line of sight and the ground is 30 degrees.
- The distance between the man's head and the bird is 25m.
Step 3: Identify the trigonometric ratio to use.
In this case, we need to use the tangent function because we have the opposite (the height of the tree) and the adjacent (the distance between the man and the tree) sides in relation to the angle.
Step 4: Use the trigonometric ratio to find the height of the tree.
The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. So, we can write:
tan(30 degrees) = height of the tree / 25m
Step 5: Solve for the height of the tree.
To find the height of the tree, we need to isolate the variable. Multiply both sides of the equation by 25m:
25m * tan(30 degrees) = height of the tree
Using a calculator, find the tangent of 30 degrees:
tan(30 degrees) ≈ 0.577
Now substitute the value:
25m * 0.577 = height of the tree
The height of the tree is approximately 14.43 meters.
Therefore, the height of the tree is approximately 14.43 meters.