Test 3 Revision – Calculators are allowed.

Pythagoras

1. Find the length of the missing sides.

2. Find the perimeter of these triangles.

A diagram may help for the following questions.

3. To wash a window that is 8 metres off the ground, Ben leans a 10 metre ladder against the side of the building. To reach the window, how far from the building should Ben place the base of the ladder?

4. A rectangular swimming pool is 21 metres wide and 50 metres long. Calculate the length of the diagonal to 1 decimal place.

5. Miss Barker is teaching a 5th grade class. She is standing 12 feet in front of Jim. Francisco is sitting 5 feet to Jim’s right. How far apart are Miss Barker and Francisco?

6. A triangle has sides with lengths of 10 metres, 16 metres and 20 metres. Is it a right-angled triangle? Explain your reasoning.

7. Find the length of the diagonal of a square of side 4cm to 2 decimal places.

8. Find the length of k.

9. Find the length of x.

Trigonometry

1. Find the lengths of sides marked x.

2. Find the size of the angles marked x.

3. ABCD is a kite. Find the length of the line

BD.

4. ABCD is a rhombus. Find the size of the

shaded angle.

5. ABC is an isosceles triangle. AC is 22cm and angle ABC is 82°.

Find the perimeter of the triangle.

Arcs and Sectors

1. Find the lengths of the major arcs.

2. Find the area of each minor sector.

3. Find the perimeter and area of the sector.

4. A pizza is cut into 5 equal slices. The diameter of the pizza was 12inches.

What area of the pizza remains after 2 slices are eaten?

5. Find the missing angles, 𝑥°, which make the given lengths of arcs and areas of sectors.

6. A circle with centre A has a sector removed.

BC is 45cm and the radius of the circle is 27cm.

a. Find the size of angle.

b. Hence, find the area of the shaded section.

Mixed Examples

1. A submarine, S, dives for 300 metres at an angle of 24° to the surface.

Calculate the depth of the submarine as shown in the diagram.

2. A wooden gate is 85 centimetres high and 200

centimetres wide. The gate is strengthened by

two bars which meet half-way across the gate as

shown. The ends of each bar measure 15

centimetres.

Calculate the length of one bar.

3. The circumference of the circle is 40·8 centimetres.

Calculate the length of the major arc AB.

4. Triangles A and B are identical right-

angled triangles. Find the perimeter

of the parallelogram.

5. Calculate the size of the shaded angle.

6. A circle with centre O is shown.

The radius of the circle is 6·4 centimetres.

Major arc AB has length 34·6 centimetres.

Calculate the size of reflex angle AOB.