Solving non-right triangles

- Case 1: knowing one side and its adjacent angles.

Example: a = 6,4    B = 55⁰    C = 82⁰

- Case 2: two sides and an angle that is opposite one of them.

Example: a = 6,2    b = 7,4    A = 48⁰

- Case 3: two sides and the angle between them.

Example:a = 5,6    b = 4,7    C = 69⁰

- Case 4: all three sides.

Example: a = 7,3    b = 6,2    c = 5,4

 

Example: two high power towers, A and B, have a lake between them. We use an auxilar point, C, to measure the distance between them and we obtain that AC = 33 metres, BC = 45 metres and the angle C = 73⁰. Calculate the distance between the towers.

 

Exercises:

1.- In 1977, men threw into space a probe for planetary research, called Voyager 2. After navigating across space for two years, it got to Jupiter's system. In that moment, the Voyager 2 was 500·10⁶ km away from Earth. The distance from Jupiter to Earth was 628.8·10⁶ km, and the angle between the observation directions of the planet and the space probe was 10^o. Calculate the distance that there was between the Voyager and Jupiter.

2.- From a point A we can see other two, B and C, with an angle of 52^o29'. We know that the distance between B and C is 450 m, and between A and B is 500 m . Find out the distance between A and C.

 

 

Solutions: 1) 161.69·10⁶ km; 2) 517.14 m