Question

In ∆ABC,P is a point on AB such that angle PCB =45°, angleB=90° and angle ACB =60° . Find the length of AP if BC =10cm.​

Answer 1

Answer:

AP= 10(√3-1) cm

Step-by-step explanation:

firstly we have to calculate AB from trig.ABC

then calculate PB from trig. PBC

then subtract PB from AB , you'll find AP

Answer 2

Answer:

AP = 10(√3 - 1) = 7.32 cm

Step-by-step explanation:

In triangle ABC,

Tan 60 = AB/BC

√3 = AB/10

AB = 10√3 cm

In triangle PBC,

Tan 45 = PB/BC

1 = PB/10

PB = 10 cm

AP = AB - PB

AP = 10√3 - 10

AP = 10(√3 - 1)

AP = 10(1.732 - 1)

AP = 10 × 0.732

AP = 7.32 cm