Trigonometry-10

From Homeworkwiki

A flag staff stands upon the top of a building at a distance of 40 m. The angles

of elevation of the tops of the flag-staff and building from that place are 60⁰

and 30⁰. Find the length of the flag-staff.

Solution: Let A be the place and B be the top of building OB.

BC is the flag-staff. C is the top of flag-staff.

From right angled triangle AOB,

OB / OA = OB / 40 = tan 30⁰

Therefore, OB = 40 tan 30⁰ = 40 / √3

From right-angled triangle AOC, OC / OA = OC / 40 = tan 60⁰

Therefore, OC = 40 tan 60⁰ = 40 √3

Therefore, Length of flag-staff = BC = OC - OB = [40√3 - 40/√3] m

= 40[√3 - 1/√3] = 40[(3 - 1)/√3] = 80/√3 = 80√3 / 3 m