Geometry: Triangles, Polygons and Transformations
The sine and cosine laws in trade contexts, angles in polygons, and translations, rotations, reflections and dilations.
12 questions, free, marked as you go with a worked explanation on every one.
What this covers
- math30 3 triangles and transformations
- sine cosine law
The questions
- A triangular brace has two sides of 14 cm and 9 cm with an angle of 62° between them. How long is the third side, in centimetres, rounded to one decimal place?
- In a triangular roof truss, angle A = 41°, the side opposite it is 18 m, and angle B = 77°. How long is the side opposite angle B, in metres, rounded to one decimal place?
- What is the measure of each interior angle of a regular octagon, in degrees?
- A quadrilateral panel has three angles measuring 95°, 118° and 74°. What is the measure of the fourth angle, in degrees?
- A template is turned 90° clockwise about a fixed point on the workbench. Which transformation is this, and what stays the same?
- A drawing of a bracket is enlarged by a dilation with a scale factor of 2.5. An edge measuring 6 cm on the original appears how long on the enlargement, in centimetres?
- A shape is reflected in a vertical mirror line. Which property of the shape changes?
- A triangular plot of land has sides of 52 m, 38 m and 66 m. Using the cosine law, find the angle opposite the 52 m side, in degrees, rounded to one decimal place.
- A triangular lot has sides of 30 m, 40 m and 50 m. Use the cosine law to find the largest angle in the lot, in degrees.
- In a triangle, angle A = 40 degrees, side a = 18 cm and angle B = 65 degrees. Use the sine law to find side b, to the nearest tenth of a centimetre.
- In a triangle, side a = 20 cm, angle A = 50 degrees and side b = 15 cm. Use the sine law to find angle B, to the nearest tenth of a degree.
- A triangle has sides a = 14 cm and b = 18 cm, with an included angle C = 55 degrees. Use the cosine law to find side c, to the nearest tenth of a centimetre.