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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