1 The angle of depression from the top of a 230-m cliff to a ship in the sea is 7°. How far is the ship from the base of the cliff? 2 A man, 1.85 m tall, stands 65 m from the base of a tree and records the angle of elevation (using an inclinometer) to the top of a tree as 17°. Find the height of the tree correct to 2 decimal places. 3 A speed boat leaves buoy A and travels in a direction of N80°E for a distance of 10.7 km to reach buoy B. It then heads due north for 11.2 km to buoy C. How far is buoy C from buoy A, correct to 2 decimal places? 4 A ship sails 30 km east, then 45 km south. Find its bearing from its starting point, correct to 1 decimal place. 5 A helicopter flies 60 km in a direction of N 72°W. How far west of the starting point is it, correct to 2 decimal places? 6 In triangle ABC, a = 17, c = 15 and C = 54°. Find two possible values of A. 7 Find the largest angle in the triangle with sides 14cm, 11cm and 17 cm. 8 Convert the following angles to radian measure. (a) 100 (b) 245 (c) 317 52 9 Convert the following radian measures to degrees and minutes (where appropriate). 7 (a) (b) 1.289c (c) 0.742c 4 10 A tomato farm is in the shape of a sector with radius 100 m and an angle of 68°. Find the length of fencing needed to enclose the farm. 11 A paddock is in the shape of a sector with an area of 1294 m2, and subtends an angle of 52°. Find the radius of the sector. 12 The angle of elevation to the top of the Rialto tower in Australia is 45° from a point on the road in the city. The elevation 75 m closer on a level straight road is 80°. How tall is the Rialto tower to the nearest metre? 13 A triathlon requires the competitors to run 500 m along a shore line from point marked A, directly north, to a point B on the shore. From point B they swim across to point C on the edge of shore. They cycle 450 m from point C directly to the starting point A. The bearing of C from A has been recorded as 068°T. (a) Write the value of angle A. (b) Find the distance the competitors had to swim, to the nearest metre. (c) Find the bearing of C from B to the nearest degree.