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To approximate the length of a marsh, a surveyor walks x = 420 meters from point A to point B. Then, the surveyor turns 75° and walks 220 meters to point C (see figure). Approximate the length AC of the marsh. (Round your answer to one decimal place.)

Answer :

Abiolataiwo2015go

If to approximate the length of a marsh, a surveyor walks x = 420 meters. The Approximate the length AC of the marsh is 420.7m.

How to find the length?

Using this formula to find the length of Ac of the march

b² = a²+c² -2ac Cos B

Where:

a²=220

c²= 420

Cos B = 180°  - 75° = 105°

Let plug in the formula

b² = 220² + 420² - 2(220)( 420) Cos  105°

b² = 220² + 420² - 2(220)( 420) (-0.258819045)

b² = 48,400 + 176,400 - 47,829.76

b² = 224,800 -  47,829.76

b = √176,970.24

b = 420.7m

Therefore the length is 420.7m

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