Initial Diagnostic Audit - Unit I1: Pythagoras' Theorem and Trigonometric Ratios
Section I1.1 - Pythagoras' Theorem
For each of the diagrams below, calculate the value of x
1.
2.
3.
4.
5. The diagram below shows the cross-section of a shed.
Section I1.2 - Further Work with Pythagoras' Theorem
For each of the diagrams below, calculate the length of the side marked x
6.
7.
8.
9. Which of these triangles is a right angled triangle?
Triangle A Triangle B Triangle C
10. A toy is made from a cone attached to a wedge, as shown in the cross section diagram below.
Section I1.3 - Sine, Cosine and Tangent
11. In the triangle below, which is the adjacent side for the angle θ ?.
Side a Side b Side c
12. For the triangle below, give the value of sinθ , cosθ and tanθ as a fraction.
13.
Use your calculator to find the angle θ to one decimal place, if sinθ = 0.65θ =
Section I1.4 - Finding Lengths in Right Angled Triangles
14. What are the values of x y
(a) x
(b) y
15. What is the length of AB in the right angled triangle below?
AB =
16. What is the value of x
x
17. What is the value of x
x
Section I1.5 - Finding Angles in Right Angled Triangles
Find the angle θ , to the nearest whole number, for each of these right angled triangles.
18.
19.
20.
21. The diagram below shows a simple bridge, supported by four steel cables.
Calculate the angles α and β shown, giving your answers to 1 d.p.
(a) α =
(b) β =
