bernhardt and julia are observing an eagles nest in a tree. Julia is 75m from the tree, and sees it at an angle of elevation of 42 degrees
A)How high up the tree is the nest
B)Bernhardt is standing 30m behind julia. At what angle of elevation does he see the nest?
A )
tan ( 42 ° ) = H / 75
H = 75 tan 42 °
H = 75 * 0.9004
H = 67.53 m
B )
tan ( theta ) = H / ( 75 + 30 )
tan ( theta ) = H / 105
tan ( theta ) = 67.53 / 105
tan ( theta ) = 0.643143
theta = 32 ° 44 ' 49 "
To find the height of the nest in the tree, we can use trigonometry. Let's assume that the distance from Bernhardt to the tree is also 75m.
A) To find the height, we can use the tangent function:
tan(θ) = opposite / adjacent
In this case, the opposite side is the height of the nest in the tree, and the adjacent side is the distance from Julia to the tree.
tan(42°) = height / 75m
height = 75m * tan(42°)
height ≈ 66.71m
Therefore, the nest is approximately 66.71m high up in the tree.
B) Now, we can find the angle of elevation from Bernhardt's position. In this case, we will use the inverse tangent (arctan) function:
arctan(opposite / adjacent) = θ
The opposite side is the height of the nest (66.71m), and the adjacent side is the distance from Bernhardt to the tree (75m + 30m = 105m).
θ = arctan(66.71 / 105)
θ ≈ 32.22°
Therefore, Bernhardt sees the nest at an angle of elevation of approximately 32.22 degrees.
To find the height of the nest, we can use trigonometry. The tangents of angles in a right triangle can be used to find the ratio of the opposite side to the adjacent side.
A) Since Julia is observing the nest from a distance, we can set up a right triangle. The height of the tree is the opposite side, and the distance from Julia to the tree is the adjacent side. Using the tangent function, we have:
tan(42°) = height of tree / 75m
Now, we can solve for the height of the tree.
height of tree = tan(42°) * 75m
Calculate the value of tan(42°) and then multiply it by 75m to get the height of the tree.
B) For Bernhardt, who is standing behind Julia, we can set up a similar right triangle. The distance from Bernhardt to the tree is the adjacent side, and the height of the tree is the opposite side. We want to find the angle of elevation at which Bernhardt sees the nest.
We can use the inverse tangent function (also known as arctan or tan^(-1)) to find the angle. Let's call it θ.
tan(θ) = height of tree / 105m (since Bernhardt is 30m behind Julia, the distance between him and the tree is 75m + 30m = 105m)
Now, we can solve for θ.
θ = arctan(height of tree / 105m)
Calculate the value of arctan(height of tree / 105m) to find the angle of elevation at which Bernhardt sees the nest.