Notice that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.



Look at the diagram below:



Triangle ABC is a 30°-60°-90° triangle. Now, in a right triangle where the angles are 30°, 60°, and 90° the sides are always in the ratio \(1 : \sqrt{3}: 2\), the leg opposite 30° (AC) corresponds with \(1\), the leg opposite 60° (BC) corresponds with \(\sqrt{3}\) and the hypotenuse AB corresponds with 2. So, \(\frac{BC}{AB}=\frac{\sqrt{3}}{2}\) --> \(\frac{BC}{70}=\frac{\sqrt{3}}{2}\) --> \(BC=35\sqrt{3}\).

Hence the leader reaches \(7+35\sqrt{3}\) above the ground.

Answer: D.

For more check Triangles chapter of Math Book: http://gmatclub.com/forum/math-triangles-87197.html

Hope it helps.


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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
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Vertical height of ladder = 70.sin(60) = 35root3

Total height = 7 + 35root3

which one of 2 angles is 60?

the question is not clear.

Since the questions says elevated at an angle of 60 deg, the base angle is 60 deg. By default, elevation is from baseline and since the ladder is placed parallel to x axis, the elevation is also from x axis.

Hope that helps!

I understand the ratio x:x(sqrt)3:2x and how to get 7+35sqrt3, but how is this not a 3-4-5 right triangle with lengths of 42-56-70? Thank you for the added explanation.

If it's 42-56-70, what is x then? Also, we get that BC, the smallest side, is \(35\sqrt{3}\) not 42.

Hope it's clear.
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We are given that the ladder of a fire truck is elevated to an angle 60 degrees above the ground and that the ladder has a length of 70 feet. We are also given that the ladder is 7 feet above the ground. The best thing to do in this situation is to draw a diagram.



Notice that the resulting triangle in the sketch is a 30-60-90 right triangle. Based on the given info, we don’t know that the ladder is leaning against a building whose side is perpendicular to the ground. The ratio of the sides of a 30-60-90 right triangle is x : x√3 : 2x. We see that the hypotenuse length of 70 feet is equal to the "2x" from the 30-60-90 ratio. Thus, we can set up an equation and solve for x.

70 = 2x

x = 35

Because x = 35, we know that the side opposite the 60-degree angle or, in this case, the height of the ladder, is 35√3. The height of the ladder is 35√3 feet and the base of the ladder is 7 feet above the ground; thus, we know that the ladder reaches a total height above the ground of 35√3 + 7 feet.

Answer D
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Answer: Option D

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