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?
To solve this problem, we can use trigonometry to determine the height of the nest and the angle of elevation for Bernhardt. Let's break down the problem into two parts:
A) Height of the nest:
To find the height of the nest, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the nest, and the adjacent side is the distance between Julia and the tree (75m).
So, we can write the equation as tan(42°) = Height of the nest / 75m.
To isolate the height of the nest, we rearrange the equation:
Height of the nest = 75m * tan(42°).
Using a scientific calculator or trigonometric tables, we can find the tangent of 42 degrees and multiply it by 75m to get the height of the nest.
B) Angle of elevation for Bernhardt:
Now, let's find the angle of elevation for Bernhardt. Since Bernhardt is standing 30m behind Julia, the distance between Bernhardt and the tree is 75m + 30m = 105m.
Using the inverse tangent function (arctan), we can find the angle of elevation for Bernhardt. The inverse tangent of a value gives us the angle whose tangent is the given value.
So, we can write the equation as Angle of elevation for Bernhardt = arctan(Height of the tree / 105m).
Now, we substitute the height of the nest (which we calculated in part A) into the equation and evaluate it using a scientific calculator or trigonometric tables to find the angle of elevation for Bernhardt.
Remember to use the correct mode (degrees or radians) when using trigonometric functions on your calculator.
By following these steps, you will be able to calculate the height of the nest and the angle of elevation for Bernhardt.