Trigonometric Ratios and Pythagoras' Theorem Exercise

These questions are for revision of Year 10 and 11 Trigonometry.

(Give all answers correct to 3 significant figures)

1. Find the lengths of the sides and angles marked by letters:

 

 

a.

 

 

b.

 

c.

 

d.

e.

f.

 

g.

h.

i.

 

j.

k.

.

 

l.

 

 

 

2. A ladder 17 m long is placed 6 m from the base of a wall. How far up the wall will the ladder reach?

3. A rectangular paddock has a diagonal 250 m long. 
The diagonal makes an angle of 34° with the long side. 
Sketch a diagram of the paddock and find the length of the short side.

4. A girl stands in one corner of a rectangular hockey field that is 110 m long and 65 m wide.
She runs diagonally across the field to the opposite corner. How far does she run?

5. A man runs 100 m in a straight line up a hill that is inclined at an angle of 13°. 
How much has he risen by at the end of his run?

6. A vertical television mast is 150 m high and is held up by wires attached to the top of the mast and to the flat ground. The wires are 200 m long. 
What angle do they make with the mast?

7. A power pole is 15 m high. It is held by wires that are connected to the top of the pole and meet the ground 9.5 m from the base of the power pole. How long are the wires and what angle do they make with the ground?