Question

in the given figure, AP perpendicular QR, angleR=30°,angle Q = 60, QR =10. The length of the shorter bisector of angle A is​

Answer 1

Answer:

QP = 2.5  cm

PS = 2.5 cm

SR = 5 cm

Step-by-step explanation:

∠A = 30° + 30° + 30° = 90°

in ΔAQR ∠A = 90°

=> Cos60° = AQ /QR

=> 1/2 = AQ/10

=> AQ = 5

in ΔAQP

Cos60° = QP/AQ

=> 1/2 = QP/5

=> QP = 2.5  cm

=> PR = QR - QP = 10 - 2.5 = 7.5 cm

in ΔAQP  & ΔAPS

AP is common

90 ° & 30° Angle common

=> ΔAPQ ≅ ΔAPS

=> QP = PS

=> PS = 2.5 cm

SR = PR - PS

=> SR = 7.5 - 2.5 = 5 cm

QP = 2.5  cm

PS = 2.5 cm

SR = 5 cm