UPSC NDA Math Model Paper 3

Given, a vertical tower stands on a declivity which is inclined at 15° to the horizon from the foot of the tower a man ascends the declivity for 80 feet. And then finds that the tower subtends an angle of 30°. From the figure, we have
By sine formula, we have

BC

sin‌75°

=

AB

sin‌30°

⇒AB=

BC×sin‌30°

sin‌75°

AB=80×

1

2

‌sin(45°+30°)
⇒AB=

40×2√2

√3+1

⇒AB=40×√2(√3+1)
⇒AB=40(√6−√2)