## Non-right-angled Triangles Exercise

Give answers correct to 3 significant figures.

1.Use the sine rule to find the side or angle marked by a letter.

 (a) (b)

2. Use the cosine rule to find a and b.

 (a) (b)

3. Find the area of the triangles.

 (a) (b)

4. Find the lengths of the sides marked by letters.

 (a) (b)

5. Find the size of the angles marked by letters.

 (a) (b)

6. Find the sizes of all of the unmarked sides and interior angles of the triangles.

 (a) (b)

7.

 (a) Find the area of the triangle ABC (b) Find the value of x, if the area of the triangle is 15 cm2.

 8. A tramper sees a building 500 metres away at a bearing of 072°. He heads due North. After 5 minutes of walking, the building is at a bearing of 120°. How many metres has he walked? If he walks at a steady speed, what is his average speed in km/h?

9. The sides of a rhombus are 8.5 cm long. The shorter side diagonal is 6.7 cm. Find the sizes of the four angles in the rhombus.

10. Find the area of an equilateral triangle of side 20 cm.

11. A farmer has an unusual field in the shape of a triangle. Two fences are 80 metres and 95 metres long and the angle between them is 95°. Find the area of the farmer's field.