Question

If ∠P measures 27°, ∠R measures 135°, and p equals 9.5, then which length can be found using the Law of Sines?

a) Length of side q
b) Length of side r
c) Length of side p
d) Not enough information to determine

Answer 1

The length of side r can be found using the Law of Sines.

Step-by-step explanation:

To use the Law of Sines, we need to have information about an angle and its corresponding side length, or two angles and a side length. In this question, we are given the measurements of angles ∠P and ∠R, and the length of side p. We can use the Law of Sines to find the length of side r. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. So, we can set up the following equation:

sin(∠P) / p = sin(∠R) / r

Substituting the given values:

sin(27°) / 9.5 = sin(135°) / r

Now, we can solve for r by cross-multiplying and rearranging the equation:

r = (9.5 * sin(135°)) / sin(27°)

Calculating the value of r:

r ≈ 5.84