In ?PQR, q = 45 cm, ?Q=117° and ?R=18°. Find the length of p, to the nearest 10th of a centimeter.

Question

In ΔPQR, q = 45 cm, ∠Q=117° and ∠R=18°.
Find the length of p, to the nearest 10th of a centimeter.

Answer 1

First line of action would be to find the missing angle P. All angles in a triangle add up to 180º so it is just a simple matter of subtracting the known angles from 180 to see what is left over

 

180 - 117 - 18 = 45

 

∠P = 45°

 

Here is where we would use what is called the sine rule. which is as follows for an ABC triangle

 

a/sin(A) = b/sin(B) = c/sin(C)

 

so on ΔPQR

 

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

 

we can now assume

 

q/sin(Q) = p/sin(P)

 

45/sin(117) = p/sin(45)

 

now we just solve for our missing side p

 

p = (45/sin(117))/sin(45)  or  p = 45/(Sin(117)*sin(45))

 

p = 71.4 cm