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M Hasan
M Hasan, Teacher
Category: Homework
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Experience:  BA (Hons) in Mathematics from Oxford University
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. A homeowner plans to cut down a dead pine tree. Because

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. A homeowner plans to cut down a dead pine tree. Because of neighbouring houses, the pine tree must fall toward the man’s own residence, which is 26 m from the base of the tree. Although it appears that falling the tree will just clear the house, he measures the angle of elevation to the top of the tree as 28°, then moves 23 m directly toward the tree and finds the new angle of elevation to be 42°. Will the tree miss the house?
Submitted: 4 years ago.
Category: Homework
Expert:  M Hasan replied 4 years ago.
Hi there!

Please refer to the following diagram:

We need to find CD which is the height of the tree.

Angle ABC = 180º - 42º = 138º

Angle ACB = 180º - 28º - 138º = 14º

Using the sine rule, we find AC:

AC/(sin 138) = 23/(sin 14)
AC = 63.616

We now calculate CD using Pythagorean theorem:

CD= √(AC^2 - AD^2)
CD = √(63.616^2 - 26^2)
CD = 58.1

Therefore, the height of the tree is 58.1 m. Hence it will not miss the house.
Customer: replied 4 years ago.
Hi, I had a problem with my Visa card, but it's resolved now.. I want to send you the figure for this question so you can revise answer with the correct letter for the angles.

Expert:  M Hasan replied 4 years ago.
I cannot see the picture. Can you send it again on mediafire like you did previously?
Customer: replied 4 years ago.
Expert:  M Hasan replied 4 years ago.
I shall post the answer shortly.
Customer: replied 4 years ago.
Expert:  M Hasan replied 4 years ago.

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