Question 3

Example 4.22. The angle of elevation from a boat at P to a point T, at the top of a vertical cliff is measured to be 30°. The

boat sails 1000 metres to a second point Q, from which the angle of elevation to T is measured to be 45°. Let R be the point

at the base of the cliff directly below 7 and let h be the height of this cliff. The bearings of R from P and Q are 050ºT and

310ºT respectively.

a) Draw a diagram expressing all this information.

b) Show that ZPRQ = 100°.

1000²

c) Show that h²=

4+2√3 sin 10°

d) Hence evaluate the height of the cliff correct to the nearest metre.