Question

At the foot of the mountain the elevation of its summit is 45 degree . After ascending 1000 m towards the mountain up a slope of 30 degree inclination the elevation is found to be 60 degree . Find the height of the mountain . For 0

Answer 1

See the attached file.

height of mountain = OA  =H

In ΔAOB,

tan (ABO) = AO/OB

⇒ tan 45 = AO/OB

⇒ 1 = AO/OB

⇒ OB = AO = H

In ΔPBR,

sin 30 = PR/PB

⇒ 1/2 = y/1000

⇒ y = 1000×(1/2) = 500m

Thus, AQ = AO - OQ = (H-500)m

cos 30 = RB/PB

⇒ √3 / 2 = x/1000

⇒ BR = 1000×(√3 / 2)

⇒ BR = 500√3m

thus OR = BO - BR = (H - 500√3)m

thus PQ = (H-500√3)m   (since OP=PQ)

In ΔAPQ,