Question

Emma is standing 10 feet away from the base of a tree and tries to measure the angle of elevation to the top. She is unable to get an accurate measurement, but determines that the angle of elevation is between 55 degrees and 75 degrees.

Answer 1

the complete question in the attached figure 

step 1
find the tree height for an angle of elevation of 55° 
tan 55°=opposite side angle 55°/adjacent side angle 55°
opposite side angle 55°=the tree height h1
adjacent side angle 55°=10 ft
so
tan 55°=h/10-------> h=10*tan 55°-----> h=14.28 ft

step 2
find the tree height for an angle of elevation of 75° 
tan 75°=opposite side angle 75°/adjacent side angle 75°
opposite side angle 75°=the tree height h2
adjacent side angle 75°=10 ft
so
tan 75°=h2/10-------> h2=10*tan 75°-----> h2=37.32 ft

therefore

the height of the tree is within the range [14.26,37.32]

Part 1) 4.2 ft

the value is not in the interval [14.26,37.32]
therefore
 it is Not Reasonable

Part 2) 14.7 ft

the value is in the interval [14.26,37.32]
therefore
 it is Reasonable

Part 3) 24.4 ft

the value is in the interval [14.26,37.32]
therefore
 it is Reasonable

Part 4) 33.9 ft

the value is in the interval [14.26,37.32]
therefore
 it is Reasonable

Part 5) 39.1ft

the value is not in the interval [14.26,37.32]
therefore
 it is Not Reasonable

Part 6) 58.7 ft

the value is not in the interval [14.26,37.32]
therefore
 it is Not Reasonable

Answer 2

The following heights are not reasonable : 4.2 feet, 39.1 feet, 58.7 feet.

The following heights are reasonable : 14.7 feet, 24.4 feet and 33.9 feet.

What is the range of the height of the tree?

The formula that can be used to determine the lower bound of the height of the tree is: tan 55 = opposite / adjacent

1.4281 = opposite / 10

Opposite = 1.4281 x 10 = 14.281 feet

The formula that can be used to determine the upper bound of the height of the tree is: tan 75 = opposite / adjacent

3.7321 = opposite / 10

3.7321 x 10 = 37.321 feet

The height of the tree is between 14.281 feet and 37.321 feet

Please find attached the complete question. To learn more about angle of elevation, please check: https://brainly.com/question/27001139