Question

Wendy is standing 60 feet away from a tree. Her eyes are 5 feet above the ground. She sees a bird hovering above a tree. The angle of elevation to the top of the tree is 25 degrees and the angle of elevation to the bird is 37 degrees. How tall is the tree? How high is the bird in the air? How far above the tree is the bird? Step by Step explanation..Please..

Answer 1

Answer:

a) The tree is 32.98 feet  tall.

b) The bird is 50.21 feet high in the air.

c) The Bird is 17.23 feet far above the Tree.

Step-by-step explanation:

From the attached diagram, please familiarize yourself with the statement drawn out and the points drawn out for better understanding.

Note that Line CD is the ground level and Line QE is the Wendy's eyes height.

1) How tall is the tree (Line BC)

line BC (tree height) => QC + QB

Line ED = QC,  ∴ QC = 5 ft

Since <BEQ = 25° and CD = QE, ∴ QE = 60ft all in triangle BEQ

Therefore Tan 25° = BQ/60

BQ = 60 (0.4663)

BQ = 27.98 ft

tree height => QC + QB = 5 ft + 27.98 ft ==> 32.98 ft

2) How high is the bird in the air? (Line AC)

line AC (bird height) => QC + QA

Line ED = QC,  ∴ QC = 5 ft

Since <AEQ = 37° and CD = QE, ∴ QE = 60ft in triangle AEQ

Therefore Tan 37° = QA/60

QA = 60 (0.7536)

QA = 45.21 ft

bird height => QC + QA = 5 ft + 45.21 ft ==> 50.21 ft

3) How far above the tree is the bird?

The difference between the bird height and the tree height = Line AC - Line BC

= 50.21 ft - 32.98 ft

= 17.23 ft