From a fixed point on the ground, the distance to a certain tree is measured to be s = 55.2 ± 0.1 m and the angle from the point to the top of the tree is measured to be θ= 0.50 ± 0.02 radians. The height of the tree is given by h = s tan θ.

a. Estimate h, and find the uncertainty in the estimate.

b. Which would provide a greater reduction in the uncertainty in h: reducing the uncertainty in s to 0.05 m or reducing the uncertainty in θ to 0.01 radians?

Step 1 of 5</p>

Here we have to find the uncertainty of the height of the tree

Given height of the tree is

The distance to certain tree is measured to be S=55.20.1 m

From this S=55.2,

The angle from the point to the top of the tree is

From this =0.5,

Step 2 of 5</p>

a) Then

h=55.2(0.5)

=30.16

Step 3 of 5</p>

Now differentiate h with respect to s and

= tan (0.5)

=0.5463

=(55.2) sec

=71.674