a tree and a flagpole are on the same horizontal ground a bird on top of the tree observes the top and bottom of the flagpole below it at 45 & 60 degrees respectively.of the tree is 10.6m high calculate the height of the flagpole
10.6/sin60 = a/sin30
a = 6.12 m.
Tan45 = y/6.12
Y = 6.12 m.
10.6-6.12 = 4.5 m. = ht. of flagpole.
please solve for me
please solve
The distance from the tree to the pole is
10.6 cot60° = 6.12 m
The height of the pole is thus 6.12(tan60°+tan45°)
To calculate the height of the flagpole, we can use trigonometry. Let's break down the problem:
1. Draw a diagram: Sketch a visual representation of the bird on top of the tree, the flagpole, and the angles mentioned.
2. Identify the given information:
- The height of the tree is 10.6m.
- The bird sees the top and bottom of the flagpole at angles of 45 degrees and 60 degrees, respectively.
3. Use tangent function: We'll use the tangent trigonometric function because we have the opposite and adjacent sides of the right triangles formed by the bird's line of sight.
- Let's calculate the height of the flagpole (opposite side) in relation to the distance from the bird to the flagpole (adjacent side) for each angle.
For the 45-degree angle:
tangent(45) = opposite / adjacent
tan(45) = h / d
h = d * tan(45)
For the 60-degree angle:
tangent(60) = opposite / adjacent
tan(60) = h / d
h = d * tan(60)
4. Calculate the distance from the bird to the flagpole:
Since the bird is on top of the tree, we can use the height of the tree as a reference point.
Let's assume the distance from the bird to the bottom of the tree is 'x,' then the distance from the bird to the top of the flagpole would be 'x + 10.6' (tree height + height of the flagpole).
5. Set up an equation:
We now have two equations with two unknowns: 'h' (height of the flagpole) and 'x' (distance from the bird to the bottom of the tree).
Using the equations from step 3 and the distance equation from step 4, we can set up an equation to solve for 'h':
x * tan(45) = (x + 10.6) * tan(60)
6. Solve the equation: Solve the equation for 'x' and substitute the obtained value back into one of the equations from step 3 to find 'h,' the height of the flagpole.
x * √2 = (x + 10.6) * √3
x√2 = x√3 + 10.6√3
x√2 - x√3 = 10.6√3
x (√2 - √3) = 10.6√3
x = (10.6√3) / (√2 - √3)
h = x * tan(45) or h = x * tan(60)
7. Calculate the height of the flagpole:
Substitute the value of 'x' obtained from step 6 into the equation for 'h' to find the height of the flagpole.
h = (10.6√3 / (√2 - √3)) * tan(45) or h = (10.6√3 / (√2 - √3)) * tan(60)