Carcass wrote:
What is the area of the triangle shown above?
A. \(\frac{25\sqrt{2}}{3}\)
B. \(\frac{25\sqrt{3}}{2}\)
C. 25
D. \(25\sqrt{2}\)
E. \(25\sqrt{3}\)
Kudos for the right answer and explanation
Since angles in a triangle must add to 180°, we can see that the missing angle is 60°, which means we have a
Special 30-60-90 Special TriangleSo let's compare the given 30-60-90 triangle with the
base 30-60-90 triangleIn the base triangle, the side opposite the 90-degree angle has length
2, and in the given triangle, the side opposite the 90-degree angle has length
1010/
2 = 5, which means the given triangle is
5 times the size of the
base triangleNow that we know the Magnification Factor, we can determine the lengths of the remaining sides.
In the
base 30-60-90 triangle, the side opposite the 30-degree angle has length
1So, in the given triangle, x = (5)(
1) =
5Likewise, in the
base 30-60-90 triangle, the side opposite the 60-degree angle has length
√3So, in the given triangle, x = (5)(
√3) =
5√3We get:
We now have enough information to find the area of a triangle.
Area of triangle = (base)(height)/2If we let side AC be the base, and let side CB be the height, then the area = (
5)(
5√3)/2 =
(25√3)/2Answer: B
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep