Diagram of a triangle PQR when QR is 14.5 <PQR=71 <QPR=57,find the lengthr of PR and PQ

the third angle R can easily be found to be 52°

then use the sine law.

I will one side, then you do the other.

PR/sin71 = 14.5/sin57°
PR = 14.5sin71/sin57 = appr. 16.3

To find the lengths of PR and PQ in triangle PQR, we can use the Law of Sines.

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In triangle PQR, we know the following information:
- QR = 14.5
- ∠PQR = 71 degrees
- ∠QPR = 57 degrees

Let's label PR as x and PQ as y.

Using the Law of Sines, we have the following ratios:

PR / sin(∠PQR) = QR / sin(∠QPR)
x / sin(71) = 14.5 / sin(57)

Now, we can solve for x (PR):

x = (sin(71) / sin(57)) * 14.5

Using a scientific calculator, we can evaluate this expression and find the value of x.

Next, let's solve for y (PQ):

PQ / sin(∠QPR) = QR / sin(∠PQR)
y / sin(57) = 14.5 / sin(71)

Similarly, we can solve for y:

y = (sin(57) / sin(71)) * 14.5

Again, using a scientific calculator, we can evaluate this expression and find the value of y.

By plugging in the values of sin(71), sin(57), and 14.5 into the respective equations, we can calculate the lengths of PR and PQ in triangle PQR.