Question

Which triangle is similar to ΔABC if sin(A) = 1/4, cos(A) = √15/4, and tan(A) = 1/√15?

Answer 1

Answer:

D is the similar triangle

Step-by-step explanation:

A quick solution to this problem is using the hypotenuse.

You know that sin(A) is 1/4 and sin is opposite / hypotenuse, so the hypotenuse should be a multiple of 4 in order for the fraction to reduce to 1/4. (it might not be, but I usually do this to see if there's a quick solution)

Using this trick, you find that the only triangle with a hypotenuse that is a multiple of 4 is the last triangle. Now simply double check the other trig. functions to check whether it truly is the same.

To check each trig function, you must first determine the corresponding angle to angle A. Again, for simplicities sake, let's use 1/4 as a determiner for the angle. The only combination of sides divided by hypotenuse that simplifies to 1/4 is 6/24. Therefore 6 must be opposite to the angle, since it's sin(a) = 1/4 and sin is opposite / hypotenuse. So the angle is X.

Now check for both cos and tan

Cos(x) = 6(15)^0.5 / 24 = (15)^0.5 / 4  CHECKS OUT

Tan(x) = 6 / 6(15)^0.5 = 1 / (15)^0.5   CHECKS OUT

Since everything checks out, then answer D is truly correct.