Morgan Park High School



Name: Non-right triangle trigonometry

1. In the diagram, triangle ABC is isosceles. AB = AC, CB = 15 cm and angle ACB is 23°.

Diagram not to scale

[pic]

Find

(a) the size of angle CAB;

(b) the length of AB.

2. The diagram shows the plan of a playground with dimensions as shown.

[pic]

Calculate

a) the length BC;

b) the area of triangle ABC.

3. The diagram shows a water tower standing on horizontal ground. The height of the tower is 26.5 m.

[pic]

From a point A on the ground the angle of elevation to the top of the tower is 28°.

a) On the diagram, show and label the angle of elevation, 28°.

b) Calculate, correct to the neatest metre, the distance x m.

4. The diagram below shows an equilateral triangle ABC, with each side 3 cm long. The side [BC] is extended to D so that CD = 4 cm.

[pic]

Diagram not to scale

Calculate, correct to two decimal places, the length of [AD].

5. The following diagram shows a triangle ABC. AB = 8 m, AC = 14 m, BC = 18 m, and [pic] = 110°.

Diagram not to scale

[pic]

Calculate

(a) the area of triangle ABC;

(b) the size of angle [pic].

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