A HOARDING ON SAVE GIRL CHILD , 5 M HIGH IS FIXED ON THE TOP OF A TOWER THE ANGLE - Maths - Some Applications of Trigonometry

Question

A HOARDING ON SAVE GIRL CHILD , 5 M HIGH IS FIXED ON THE TOP OF
A TOWER THE ANGLE OF ELEVATION OF THE TOP OF THE HOARDING AS
OBSERVED FROM PT A ON GROUND IS 60 AND THE ANGLE OF D OF POINT A
FROM THE TOP OF THE TOWER IS 45 FIND THE HEIGHT OF THE TOWER USE
ROOT 3 = 1 73

Ajanta Trivedi · Accepted Answer

let the height of tower be AB = h m let AD be the hoarding such that AD = 5 m let C be the observation point such that the angle of elevation of the top of the hoarding i e âˆ BCD= 60 deg the angle of depression of the observation point C from A be âˆ PAC=âˆ ACB = 45 deg therefore in the triangle ABC, $\tan 45 = \frac{A B}{B C} 1 = \frac{h}{B C} \Rightarrow B C = h m (1)$ in the triangle DBC, $\tan 60 = \frac{D B}{B C} \sqrt{3} = \frac{h + 5}{h} [∵ D B = D A + A B = 5 + h] \sqrt{3} h = h + 5 (\sqrt{3} - 1) h = 5 h = \frac{5}{\sqrt{3} - 1} = \frac{5}{\sqrt{3} - 1} * \frac{\sqrt{3} + 1}{\sqrt{3} + 1} h = \frac{5 (\sqrt{3} + 1)}{2} = \frac{5}{2} (1 73 + 1) = \frac{5}{2} * 2 73 h = 6 825 m$ thus the height of the tower is 6 825 m hope this helps you cheers!!

A HOARDING ON SAVE GIRL CHILD , 5 M HIGH IS FIXED ON THE TOP OF A TOWER THE ANGLE OF ELEVATION OF THE TOP OF THE HOARDING AS OBSERVED FROM PT A ON GROUND IS 60 AND THE ANGLE OF D OF POINT A FROM THE TOP OF THE TOWER IS 45 FIND THE HEIGHT OF THE TOWER USE ROOT 3 = 1.73