# trig problems

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```					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

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.

```
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 views: 11 posted: 5/27/2011 language: English pages: 1