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In our next post, we’ll talk about how 30-60-90 triangles can be used directly to calculate the area of equilateral triangles. This gives you the opportunity to be preemptive and use the test’s patterns against itself. Notice that the first two answers feature a √3 and a √2 term, and this is clearly a geometry question. In terms of strategy, another point: a brief look at the answer choices at the start of the problem gives a strong hint that either a 30-60-90 or 45-45-90 triangle is involved. Notice that at this point, it’s up to you to make the deduction that we have a 30-60-90 triangle, and thus the distance from the right angle marker to point R must be 5√3:įrom there, it’s straightforward to see that RS is simply the marked length of 10 minus the length of 5√3 we just deduced, thus leading us to answer choice A. Similarly, in this Official Guide problem, we are told that VR is length 10:
That’s much more the kind of critical thinking the GMAT is interested in testing. So even without labeled angles:Ī right triangle with a hypotenuse twice the length of one of its legs must be a 30-60-90 triangle. That guarantees that the third side fits the √3 component of our ratio, giving that side a length of 5√3. The hypotenuse is twice the length of one of the sides, giving them a 2:1 ratio. Furthermore, did you identify anything that gives this away as a 30-60-90?
But we do have 2 sides and 1 angle in total, which is sufficient to form a unique triangle. Notice we are given no angles except the right angle. To understand this problem, let’s first talk about one of the higher-level ways the GMAT could test 30-60-90 triangles. Always simplify the question as quickly as possible.) Remember that the GMAT is very good at using complicated wording to frame a simple concept. (For starters, notice that the question they’re asking for - the distance between the actual position and the perceived position - is just line segment RS. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the object? From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. In the figure above, V represents an observation point at one end of a pool. This is low-level memorization, and we can deduce that the side opposite the 60-degree angle will be length 5√3, while the hypotenuse will be length 10.īut let’s look to this GMAT Official Guide problem to see something a little more high-level. For example, Suppose we are given the following information: Now, it’s easy enough to memorize this ratio and deduce what each side length will be, given that we are dealing with a 30-60-90 triangle. And it’s worth noting, as with all triangles, that the shortest side is opposite the smallest angle, while the longest side is opposite the largest angle, etc. Like the isosceles right, its sides always fit a specific ratio, as seen in the above diagram (1 : √3 : 2). There is another so-called “special right triangle” commonly tested on the GMAT, namely the 30-60-90 right triangle. In a previous piece, we covered the 45-45-90 right triangle, also known as the isosceles right triangle. Date: 7th January, 2021 30-60-90 Right Triangle
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