Question

At the foot of a mountain the elevation of its summit is 45 degree after ascending 100m towards the mountain up a slope of 30

Answer 1

Math

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)