2.5 Further Applications of Right Triangles

This group of problems is much more demanding in the sketches and the algebra involved to find solutions!!

Bearing used in navigation and there are two common methods used

Method 1 Only an angle is given. This angle is measured clockwise with 0^o as due North

41^o 152^o 215^o 311^o

Important - Drawing an accurate, well-labeled sketch is extremely important!!!

Example

Radar stations A and B are on an east-west line, 8.6 km apart. Station A detects a plane at C, on a bearing of 53^o. Station B simultaneously detects the same plane on a bearing of 323^o. Find the distance from B to C. (ans: 5.2 km)

Method 2 The measurement includes North or South and East or West

N 16^o E S 25^o E S 48^o W N 47^o W

Example The bearing from A to C is N 64^o W. The bearing from A to B is S 82^o W. The bearing from B to C is N 26^o E. A plane flying at 350 mph takes 1.8 hr to go from A to B. Find the distance from B to C. (ans: 350 mi)

More Angles of Elevation

Maria needs to find the height of a building. From a given point on the ground, she finds that the angle of elevation to the top of the building is 74.2^o. She then walks back 35 ft. From the second point, the angle of elevation to the top of the building is 51.8^o. Find the height of the building. (ans: approx 69 ft)