4. A tree service is to fell a tree. A rope is attached to the top of the tree to determine the direction in which the tree
will fall. The rope meets the top of a 6-foot tall light pole that is 20 feet away from the tree. The rope hits the ground 10
ft on the other side of the light pole (away from the tree). There is concern the when the tree falls it will damage the
light pole.
a. How tall is the tree?
b. Will the tree hit the light pole when it falls?

a) The tree is 18 feet tall

b) No, 18 feet is less than 20 feet

Step-by-step explanation:

See attached picture as part of the solution.

a)

Let the tree height be X

The total Triangle ABC has been Interpreted from illustration.

Use the smaller triangle to find "Angle B"

Tan B = Opposite (6 ft) / Adjacent (10 ft)

Tan B = 0.6 ft

B = Tan⁻¹(0.6)

B = 30.9°

Since the smaller and bigger triangle has the same base angle B

∴ Tan 30.9° = X / 30

0.6 = X / 30

Multiply both sides by 30

0.6 x 30 = X

X = 18 ft

∴ The tree is 18 feet tall.

b)

The distance of the pole from the tree is 20 feet and the tree height is 18 feet. When the tree falls, the tree will not hit the pole because the length of the tree is shorter than the distance of the pole from the tree.

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step-by-step explanation: