You are wondering how high that hawk is, surveying your back yard from a perch a

Question

You are wondering how high that hawk is, surveying your back yard from a perch at the top of an oak tree toward the back property line. Remembering that you learned about vectors in physics, you measure off two components of a vector from your feet to the bird. Let "x" be parallel to the back of your house, and "y" perpendicular to the house out to the base of the tree. The vector to the bird would be (x, y, z). If x is 43 and y is 70 meters, what would z be in meters such that the angle from your feet to the bird is 45 degrees?

Explanation / Answer

given
x is parallel to back of the house
y is in the direction of the tree
z is upwards

x = 43 m
y = 70 m
theta = 45 deg
hence
distance from bird = d
dcos(theta) = y
dsin(theta) = z

for theta = 45 deg
y = z = 70 m

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