Bunuel wrote:
ficklehead wrote:
What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?
A. 24 sq units
B. 48 sq units
C. 24*root3
D. 48*root3
E. Such a triangle does not exist
Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.So, we are expected to solve this problem in the following way:
Attachment:
Triangle.png
Notice that triangle ABD is 30°-60°-90° right triangle. Now,
in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).
Next, the area of triangle ABC equals to the area of triangle ACD
minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).
Answer: A.
.
I would like to make two quick points:
1. Once you have found out the height of the triangle (AD), which is 4 here, you could have found out the area of the required triangle(ABC) simply by multiplying half of the height AD (1/2*4) and base BC (12) instead of using such a long method of find the area of ACD and subtracting from it the area of ABD.
2. Its irrelevant whether one is memorizing/using this formula (\(1:\sqrt{3}:2\) ) or memorizing/using trigonometric tables ( Although I feel knowledge of basic trigonometry is more handy), as all these formulas are interrelated. I just feel that students should be given the choice between the two. Hence, such basic trigonometry should be included in the prep materials.