Cosine Law Problems

Solve problems using the cosine law; a tutorial with detailed solutions and exercises with answers.

Problem 1

A triangle has sides equal to 5 cm, 10 cm, and 7 cm. Find its angles (round answers to 1 decimal place). Solution to Problem 1:

Problem 2

An aircraft tracking station determines the distance from a common point \( O \) to each aircraft and the angle between the aircrafts. If the angle \( O \) between the two aircrafts is \( 49^\circ \) and the distances from point \( O \) to the two aircrafts are 50 km and 72 km, find the distance \( d \) between the two aircrafts (round answers to 1 decimal place).

Solution to Problem 2:

Exercises

1. A triangle has sides equal to 4 m, 11 m, and 8 m. Find its angles (round answers to 1 decimal place).

2. A ship leaves port at 1 pm traveling north at the speed of 30 miles/hour. At 3 pm, the ship adjusts its course 20 degrees eastward. How far is the ship from the port at 4 pm? (round to the nearest unit).

Solutions to Above Exercises

1. \( A = 129.8^\circ \), \( B = 34.0^\circ \), \( C = 16.2^\circ \)
2. 89 miles.

More References to Cosine and Sine Laws and Geometry

Cosine Law Calculator and Solver
Geometry Tutorials, Problems and Interactive Applets
Sine Law Problems
Sine Law Calculator and Solver