LAW OF COSINE WORD PROBLEMS

The cosine law can be used which is not a right triangle.

a² = b² + c² - 2bc cos A

b² = c² + a² - 2ac cos B

c² = a² + b² - 2ab cos C

Problem 1 :

Peter has three sticks measuring 19 inches, 23 inches, and 27 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by the 19 inch and 23 inch sides to the nearest degree.

Solution :

The side which is opposite to angle measure A is named as a, B as b and C as c.

∠A = ?, AB = c = 19 inches, BC = a = 27 inches, AC = b = 23 inches

Problem 2 :

Mary is orienteering across a large flat plain from Marker A to Marker B which are 4 miles apart. After walking 1.8 miles she realizes she is 6° off-course. To the nearest tenth of a mile, how far from Marker B is she when she realizes her error?

Solution :

∠A = 6 degree, AC = b = 1.8 miles, BC = a = ?, AB = c = 4 miles

Problem 3 :

A farmer has a field in the shape of a triangle. The farmer has asked the manufacturing class at your school to build a metal fence for his farm. From one vertex, it is 435 m to the second vertex and 656 m to the third vertex. The angle between the lines of sight to the second and third vertices is 49^o. Calculate how much fencing he would need to enclose his entire field.

Solution :

∠A = 49 degree, AC = b = 656 m, BC = a = ?, AB = c = 435 m

Perimeter = a + b + c

= 458 + 656 + 435

= 1549 m

Problem 4 :

A bicycle race follows a triangular course. The 3 legs of the race are, in order, 2.3 km, 5.9 km and 6.2 km. Find the angle between the starting leg and the finishing leg, to the nearest degree.

Solution :

∠A = ?, AC = b = 6.2 km, BC = a = 5.9 km, AB = c = 2.3 km

Problem 5 :

You’ve been given an assignment to mill a triangular shape on the CNC machine for a contemporary sign for the arts department. The dimensions you’re given by your manufacturing teacher are shown in the following diagram. What is the measurement of TS?

Solution :