VCE General Maths (Further) Unit 1

Trigonometry

2014 Test

Name: _______________________________

Total: / 28 marks ( %)

Conditions: 45 min, Casio Calculator and Double sided handwritten Summary Sheet permitted

Multiple Choice Section ( 6 x 2 marks = 12 marks)

1. A bearing of S20 °W is equivalent to:

A. 020 °T B. 200 °T C. 160 °T D. 120 °T E. 340 °T

2. A 7m ladder is leaning against a vertical wall with its base on level ground. The ladder reaches a height of 6m up the wall. The distance from the foot of the ladder to the foot of the wall is closest to:

A. 2.7m B. 2.5m C. 3.6m D. 3.8m E. 4.1m

3. The value of x , to 2 decimal points is;

A. 5.00 B. 5.07 C. 5.11 D. 5.88 E. 8.62

30.45 °

10

x

4. A triangle has side lengths of 5m, 6m, and 7m. The largest angle in this triangle is closest to:

A. 75 °B. 88 °C. 62 °D. 57 °E. 78 °

5. Using the following diagram, the length of line BD is closest to,

A. 3.70 cmB. 5.38 cmC. 5.74 cmD. 6.69 cmE. 9.74 cm

6. A farmer travels from point A to point B on a bearing of 060 °T . If he wishes to turn around and return to point A from point B he will need to travel on a bearing of:

A. 160 °TB. 240 °TC. 260 °TD. 300 °TE. 280 °T

D C

6cm

B

76 °

48 °

/

Short Answer Section. Show ALL working.

Question 1

Find the area of this isosceles triangle to two decimal places.

(2 marks)

Question 2A step ladder with legs the same length stands on the floor with its feet 1.5m apart. If the angle formed by the legs is 50 ° how high above the floor is the top of the ladder, to one decimal place?

(3 marks)

10cm

8cm

50 °

1.5m

Question 3

In triangle ABC , A=108.6 ° ,b=9cm and c=8cm. Find the length of side a, to 2 decimal places.

(2 marks)

Question 4

A plane flying at an altitude of 5000m is preparing to land at Tullamarine Airport. The plane is directly in line with the runway and the angle of depression from the plane to the start of the runway is 12 °.

a. Draw a neat diagram of this situation (include all known measurements)

(1 mark)

b. The plane now begins its decent. How far must the plane fly, in a straight line, in order to reach the start of the runway? (Give your answer to the nearest metre)

(2 marks)

Question 5

A yacht has a triangular sail. The sail is an irregular triangle with side lengths DE = 2.7m and EF = 10.6m and angle EDF=130 °. Calculate the area of the sail correct to 2 decimal places. (Include a diagram of the sail with all known measurements)

(3 marks)

Question 6

A hiker travels 18 kilometres on a bearing of 070 °T and then turns onto a bearing of 030 °T for 25 kilometres.

a. Draw a diagram for this situation including all known measurements.

(1 mark)

b. Calculate how far the hiker is from her starting point? (Give your answer to one decimal point)

(2 marks)

THIS IS THE END OF THE ASSESSMENT