b = 17
Step-by-step explanation:
Step 1:
Given PQ = QR in triangle PQR.
So, triangle PQR is an isosceles triangle.
Hence, [tex]\angle \mathrm{QPR}=\angle \mathrm{QRP}=47^{\circ}[/tex] – – – – (1)
Step 2:
Let us consider two triangles PQS and SQR.
[tex]\angle \mathrm{PQS}=\angle \mathrm{SQR}=\mathrm{a}[/tex] (given angle)
PQ = QR (given side)
[tex]\angle \mathrm{QPS}=\angle \mathrm{QRS}=47^{\circ}[/tex] (angle proved in equation (1))
[tex]\therefore \Delta PQS=\Delta SQR[/tex] (by ASA congruence criterion)
Hence by corresponding parts of congruence triangles,
⇒ PS = SR
⇒ PS = 17
⇒ b = 17
Hence the value of b is 17.
