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A ladder of a fire truck is elevated to an angle of 60° and
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10 Jun 2020, 10:10
10 Jun 2020, 10:10
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A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?
(A) 35
(B) 42
(C) \(35\sqrt{3}\)
(D) \(7 + 35\sqrt{3}\)
(E) \(7 + 42\sqrt{3}\)
(A) 35
(B) 42
(C) \(35\sqrt{3}\)
(D) \(7 + 35\sqrt{3}\)
(E) \(7 + 42\sqrt{3}\)
Re: A ladder of a fire truck is elevated to an angle of 60° and
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10 Jun 2020, 10:10
10 Jun 2020, 10:10
Expert Reply
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Re: A ladder of a fire truck is elevated to an angle of 60° and
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10 Jun 2020, 10:21
10 Jun 2020, 10:21
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Carcass wrote:
A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?
(A) 35
(B) 42
(C) \(35\sqrt{3}\)
(D) \(7 + 35\sqrt{3}\)
(E) \(7 + 42\sqrt{3}\)
(A) 35
(B) 42
(C) \(35\sqrt{3}\)
(D) \(7 + 35\sqrt{3}\)
(E) \(7 + 42\sqrt{3}\)
Here's an idea of what's going on....
When we compare the big triangle with the BASE 30-60-90 special triangle (which you must memorize for test day!), we can see that the hypotenuse of the big triangle is 35 times as long as the hypotenuse of the base triangle.
This means the big triangle is 35 times the size of the base triangle.
This means that, on the big triangle, the side opposite the 60 degree angle must be 35√3
Now before we (incorrectly) choose answer choice C, we must keep in mind that the question tells us the base of the ladder is 7 feet above the ground...
So, the TOTAL distance from the top of the ladder to the ground = 35√3 + 7
Answer: D
Cheers,
Brent
