In triangle PQR, angle P is 20 degres, angle R is 150 degrees, and QR is 6, the length of PQ is...?
simple application of the sine law
PQ/sin150 = 6/sin20
PQ = 6sin150/sin20
= ....
To find the length of 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.
Let's denote the length of PQ as x. We can use the following proportion:
Sin(P) / PQ = Sin(R) / QR
Plugging in the given values, we get:
Sin(20) / x = Sin(150) / 6
To find the value of x, we can cross-multiply:
Sin(20) * 6 = Sin(150) * x
Now, let's solve for x:
x = (Sin(20) * 6) / Sin(150)
Using a calculator, we find that Sin(20) = 0.342, and Sin(150) = 0.866. Plugging these values into the equation, we get:
x = (0.342 * 6) / 0.866
x ≈ 2.37
Therefore, the length of PQ is approximately 2.37 units.