Question

How many distinct triangles can be formed for which mZX = 51°, x = 5, and y = 2?

zero
one
two

Answer 1

From the law of sines, we have:

,

where x and y are the sides opposite to angles X and Y, respectively.

Substituting the known values, we have:

, thus

.

Using a calculator, we can find that arcsin(0.31)=18 degrees, approximately.

We know that sine of (180-18)=162 degrees is also 0.31. But 162 and 51 degrees add up to more than 180 degrees.

Thus, there is only one triangle that can be formed under these conditions.

Hope this helps!

Explanation:

Answer 2

From the law of sines, we have:

,

where x and y are the sides opposite to angles X and Y, respectively.

Substituting the known values, we have:

, thus

.

Using a calculator, we can find that arcsin(0.31)=18 degrees, approximately.

We know that sine of (180-18)=162 degrees is also 0.31. But 162 and 51 degrees add up to more than 180 degrees.

Thus, there is only one triangle that can be formed under these conditions.

Hope this helps!