A TREE AND A FLAGPOLE ARE IN THE SAME GROUND.A BIRD ON TOP OF THE TREE OBSERVERS THE TOP AND BOTTOM OF THE FLAGPOLE BELOW IT AT ANGLES OF 46 AND 60 DEGREES RESPECTIVELY. IF THE TREE IS 10.65m HIGH WHAT IS THE HEIGHT OF THE FLAGPOLE
Draw a diagram.
The distance x between the tree and pole can be found using
10.65/x = tan60°
Then the remaining height y of the top of the tree and the top of the pole is found by
y/x = tan46°
To find the height of the flagpole, we can use trigonometry. Let's assume the height of the flagpole is represented by h.
From the bird's perspective, it sees the top of the flagpole at an angle of 46 degrees and the bottom of the flagpole at an angle of 60 degrees.
We can use the tangent function to find the height of the flagpole. The tangent of an angle is equal to the opposite side divided by the adjacent side.
For the top angle of 46 degrees:
tangent(46 degrees) = h / 10.65m
For the bottom angle of 60 degrees:
tangent(60 degrees) = (h + 10.65m) / 10.65m
Now, let's solve these equations to find the height of the flagpole.
Using a scientific calculator or trigonometric tables, we can find the tangent values for 46 degrees and 60 degrees, which are approximately 1.0355 and 1.7321 respectively.
First equation:
1.0355 = h / 10.65m
Multiplying both sides by 10.65m:
10.65m * 1.0355 = h
h ≈ 11.02m
Second equation:
1.7321 = (h + 10.65m) / 10.65m
Multiplying both sides by 10.65m:
10.65m * 1.7321 = h + 10.65m
Simplifying:
18.41m = h + 10.65m
Subtracting 10.65m from both sides:
7.76m = h
So, the height of the flagpole is approximately 7.76 meters.