CSOINE LAW WORD PROBLEMS WORKSHEET

Problem 1 :

Calculate the perimeter of triangle ABC.

Solution

Problem 2 :

Boat A is 16 km from a lighthouse on a bearing of 055°. Boat B is 11 km from the same lighthouse on a bearing of 152°. Calculate the distance between the two boats.

Solution

Problem 3 :

Shown is sector OAB.

O is the centre of the circle with radius 9 cm.

A and B are points on the circle.

The length of the chord AB is 10.35 cm.

Find the area of sector OAB.

Solution

Problem 4 :

A hot air balloon is flying above two point, standing on the ground at points A and B, 600m apart.

The hot air balloon is 300 m from A and 500 m from B.

(a) Work out the angle of elevation from point B.

(b) How high is the hot air balloon from the ground?

Solution

Problem 5 :

A boat, located at position X is running out of fuel.

There are two ports located at Y and Z.

The boat must refuel as soon as possible.

How much closer is the boat to the port at Y than the port at Z?

Solution

Answer Key

1)  the perimeter of triangle ABC is 21.5 cm.

2)  the distance between the two boat is 18.94 km.

3)  38.78 cm²

4)  a)  ∠B=30°     b)   h=200√14/3 m

5)  From X to Z is 4.62 miles closer then X to Y.