Page 54 - modul trigonometri bilingual

Example 4.2

Global Positioning System (GPS) is a system for determining the

location of objects on the earth's surface with the help of satellite
signals. On mobile phones with GPS, an approximate location of the
phone can be given before the GPS signal is received. Suppose there

are two cell phone signal transmitter towers within range of the
phone. The two towers are located 3000 m apart along the straight
highway. Based on the signal delay, it can be determined that the

mobile phone is 2000 m away from the first tower and 2000√2 m of
the second tower. Determine the distance of the phone from the
highway.

Alternative Solutions

The problem can be described as follows.

Use the cos rule:

2
2
2
BC = AB + AC – 2 x AB x AC x cos< BAC
2
2
2
⇔ (2000√2) = 3000 + 2000 − 2 × 3000 × 2000 × cos
⇔ 4000000 × 2 = 9000000 + 4000000 − 12000000 cos

⇔ 8000000 = 9000000 + 4000000 − 12000000 cos

⇔ 12000000 cos = 9000000 + 4000000 − 8000000

⇔ 12000000 cos = 5000000

5000000 5
⇔ cos = =
12000000 12
5
From cos = can be described triangles on the side and obtained:
12

2
2
= √12 − 5 = √119

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