A surveyor stands on level ground at a point (D )

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Trigonometry · Applications of Trigonometry

Problem

A surveyor stands on level ground at a point

D

, which is

70\,\text{m}

horizontally from the foot

C

of a vertical cliff

AB

. Using a laser range-finder, the straight-line distance from

D

to the top of the cliff

A

is measured to be

85\,\text{m}

. (a) Find, correct to the nearest minute, the angle of elevation of the top of the cliff as observed from

D

. (b) Using the result from part (a), calculate the height of the cliff

AB

to the nearest tenth of a metre. (c) The surveyor then walks directly towards the cliff for

40\,\text{m}

to a new point

E

. Without re-measuring any distances, determine the angle of elevation of

A

from

E

and state, with justification, whether it is more than, equal to, or less than

40^\circ