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Applications of Non-Right Triangles

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Applications of Non-Right Triangles

EQ: How can I use my knowledge of the sine and cosine rules to solve real world problems involving unknown lengths and angles?

1. Two ships leave a harbor at the same time. The first steams on a bearing 045° at 16kmh-1, and the second on a bearing of 305° at 18kmh-1. How far apart will they be after 2 hours?

18km/h

16km/h

36 km

32km

55°

45°

305°

Given the information, what rule do we use?

The Cosine Rule!

x km

36km

32km

100°

x2 = 362 + 322 – 2(36)(32)cos(100°)

x = 52.2 km

2. A short course biathlon meet requires the competitors to run in the direction S60°W to their bikes and then ride S40°E to the finish line, situated 20 km due South of the starting point. What is the distance of this course?

60°

Total angle measurement = 80°

30°

20 km

50°

40°

Which rule should you use to solve for the unknown lengths?

x km

60°

The Sine Rule

20 km

80°

y km

x + y = 30.64 km

3. A surveying team is trying to find the height of a hill. They take a ‘sight’ on top of the hill and find that the angle of elevations is 23°27’. They move a distance of 250 meters on level ground directly away from the hill and take a second ‘sight’. From this point, the angle of elevation is 19°46’. Find the height of the hill, correct to the nearest meter.

19°46’

h

250 m

23°27’

With the given information, what rule(s) should we use to solve for x, and subsequently, h?

x

Sine Rule and then Trig Ratio (Sine)

h

19°46’

23°27’

x = 1548.63…

h = 523.73 meters so, to 3 significant figures,

524 meters

180° - 23°27’ = 156°33’

250 m

Mrs. Holst, the fastest runner east of the Mississippi, takes off for her daily sprint. First, she runs due South for 1.5 hours travelling 20 miles per hour. She then turns N70°E and runs for 45 minutes at the same rate.

a) At the end of 2.25 hours, how far is she from home? b) If she runs at the same pace straight home, will she make it home within 3 hours?

c) How many total miles did she run?