A ladder of a fire truck is elevated to an angle of 60° and

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.

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

Answer: Option D

Video solution by GMATinsight

Hello guys,

I don't really understand the level of difficulty of this question. I bought the official guide and its questions are separated into easy, medium and hard, so I guessed the hard ones would be around 700. However, every time I check a question of these on gmatclub it says "Level: sub-600".

Can someone please explain this?

The difficulty level of a question on our site is calculated automatically based on the timer stats from the users which attempted the question. So, the difficulties here and in OG's might not coincide.

Video solution from Quant Reasoning:
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Can this question show up in the GMAT focus edition or we can skip practicing it?

Since hardcore geometry is no longer a part of the GMAT, I’d say it’s unlikely that you’ll encounter such questions on the test.