Question

In ΔPQR, r = 38 cm,

�
m∠P=49° and
�
m∠Q=127°. Find the length of p, to the nearest centimeter.

Answer 1

Rounding to the nearest centimeter, we get p ≈ 57 cm.

Explanation:

We are given a triangle ΔPQR with r = 38 cm, m∠P = 49°, and m∠Q = 127°. We are asked to find the length of side p.

First, let's find m∠R:

m∠R = 180° - (m∠P + m∠Q)

m∠R = 180° - (49° + 127°)

m∠R = 180° - 176°

m∠R = 4°

Now, we have all three angles of the triangle: P = 49°, Q = 127°, and R = 4°. We can use the Law of Sines to find the length of side p:

p/sin(P) = r/sin(R)

Let's plug in the known values:

p/sin(49°) = 38/sin(4°)

Now, solve for p:

p = (sin(49°) * 38) / sin(4°)

p ≈ 56.96 cm

Rounding to the nearest centimeter, we get p ≈ 57 cm.