Initial Diagnostic Audit - Unit I2: Trigonometric Problems
Section I2.1 - Mixed Problems Using Trigonometry
1. A weather balloon is at a height of 900 metres.
The angle of elevation of the balloon from an observer on the field is 42°.
What is the distance of the balloon from the observer, correct to the nearest metre?

Distance = m

2. What is the size of the angle labelled p? Give your answer correct to the nearest degree.

p = °

3. What is the size of the angle labelled q? Give your answer correct to the nearest degree.

q = °

4. The diagram shows a symmetrical framework for a bridge.
AC = 100 m, AB = BC = 70 m

(a)  Calculate the angle BAD, giving your answer to the nearest degree.  ∠BAD = °

(b)  Calculate the length DE, giving your answer to the nearest m.  DE = m

Section I2.2 - Sine and Cosine Rules
5. Calculate the value of x in the triangle below, giving your answer to 1 d.p.

x = cm

6. Calculate the value of θ in the triangle below, giving your answer to the nearest degree.

θ = °

7. Calculate AC for the triangle below, giving your answer to 1 d.p.

AC = cm

8. Calculate the length of the side marked x in the triangle below. Give your answer to 1 d.p.

x = cm

9. Calculate the angle θ as shown in the triangle below. Give your answer to the nearest degree.


θ = °

Section I2.3 - Application: Area of Any Triangle

Find the area of the shaded region in each of the following figures, giving your answers to 1 d.p.
10.

Area = cm2

11.

Area = cm2

12.

Area = cm2

13. O is the centre of circle, radius 4 cm.

Area = cm2

14. O is the centre of circle, radius 7 cm.

Area = cm2

Section I2.4 - Heron's Formula

Calculate the areas of the following triangles, giving your answers to 1 d.p.
15.

Area = cm2

16.

Area = cm2

17.

Area = cm2

18.

(a)  What is the area of the triangle above? Give your answer to 1 d.p.  Area = cm2

(b)  What is the angle shown by θ in the triangle? Give your answer to the nearest degree.  θ = °

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Produced by Russell Geach for CIMT - August 2014