A tall lamp-post stands on the edge of a straight river
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Trigonometry · Applications of Trigonometry
Problem
A tall lamp-post stands on the edge of a straight river. From point R directly opposite the lamp-post on the other bank, the angle of elevation of the top of the lamp-post is 60°. After rowing a boat 20 m directly away from the bank to point S along the same straight line, the angle of elevation of the top becomes 30°.
Use this information to answer the questions below.
(i) If the width of the river is x metres and the height of the lamp-post is h metres, write two trigonometric equations linking x and h. Clearly state which observation gives each equation.
(ii) Solve the simultaneous equations to find the width of the river.
(iii) Hence determine the height of the lamp-post, giving your answer correct to one decimal place.