christopher sees a bird in a tree at an angle of elevation of 50 degree. After walking 30 feet further from the tree, he views the bird at an angle of elevation of 35 degree. how high in the tree, to the nearest tenth of a foot, is the bird sitting?
To solve this problem, we can use trigonometry and set up a right triangle. Let's assume the height of the tree is represented by 'h' (in feet).
From Christopher's perspective, the bird, the top of the tree, and Christopher himself form a right triangle. The angle of elevation of 50 degrees corresponds to the angle opposite the side representing the height of the tree.
Now, let's break down the problem into two parts:
Part 1:
In the first scenario, when Christopher is closer to the tree, the angle of elevation is 50 degrees. In this case, the side opposite the 50-degree angle is equal to the height of the tree, 'h'.
tan(50°) = h / x
Where 'x' represents the distance between Christopher and the tree.
Part 2:
In the second scenario, Christopher walks 30 feet further from the tree. The angle of elevation is now 35 degrees. In this case, the side opposite the 35-degree angle is still equal to the height of the tree, 'h'. However, the distance between Christopher and the tree is now 'x + 30'.
tan(35°) = h / (x + 30)
Now that we have set up the two equations, we can solve for 'h'.
We can rewrite the first equation as:
h = x * tan(50°)
And the second equation as:
h = (x + 30) * tan(35°)
Since both expressions represent the height 'h', we can set them equal to each other and solve for 'x':
x * tan(50°) = (x + 30) * tan(35°)
Now we can solve this equation to find the value of 'x'.
After finding the value of 'x', we can substitute it back into either of the initial equations to calculate the height 'h'. Rounding to the nearest tenth of a foot, we can find the height of the bird in the tree.
draw a diagram.
study your basic trig functions.
You can see hat if the height is h, then
h cot35° - h cot50° = 30
Now just solve for h