Sam and Markus are standing on level ground 100m apart. A large tree is due North of Markus and on a bearing of 065degrees from Sam. The top of the tree appears at an angle of elevation of 25 degrees to Sam and 15 degrees to Markus. Find the height of the tree.
To find the height of the tree, we can use trigonometry. Let's denote the height of the tree as "h".
From Sam's perspective, let's draw a right triangle with the tree top, Sam, and the base of the tree. The angle of elevation from Sam's point of view is 25 degrees. The opposite side of the triangle is the height of the tree "h," and the adjacent side is the distance between Sam and the tree base.
Using trigonometry, we can use the tangent function: tan(angle) = opposite/adjacent.
tan(25 degrees) = h / 100m
Rearranging the equation, we can solve for h:
h = 100m * tan(25 degrees)
Now, let's calculate the value:
h = 100m * tan(25 degrees)
h ≈ 45.52m
Therefore, the height of the tree is approximately 45.52 meters.