MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Trigonometry · Applications of Trigonometry
Problem
A surveyor’s eye is 1.6 m above horizontal ground. From this position, the angle of elevation of the top of a tower is 28°. The foot of the tower is 85 m from the surveyor.
(i) For a right-angled triangle having horizontal side d and angle of elevation θ, show that the vertical height h of the object is given by h=dtanθ.
(ii) Using the result of part (i), find the height of the tower to the nearest centimetre.
(iii) If the surveyor walks back so that the horizontal distance becomes 105 m, calculate the new angle of elevation of the top of the tower, correct to the nearest degree.