the quadrilateral PQRS shows the boundary of a forest.a straight 15 km road goes due east PToR.a) the bearing of S from P is 030° and PS=7km.1) write down the size of angle SPR.2) calculate the lenth of RS.
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the quadrilateral PQRS shows the boundary of a forest.a straight 15 km road goes due east PToR.
Consider the figure while going through the following steps.
1) write down the size of angle SPR.
∠ SPR = 90° - ∠ SPN
∠ SPR = 90° - 30°
∴ ∠ SPR = 60°
2) calculate the lenth of RS.
cos 30° = PN/PS
√3/2 = 7/PS
PS = 14/√3
∴ PS = 8.08 km
cos P = [ PS² + PR² - RS²] / [ 2(PS)(PR) ]
cos 60° = [ 8.08² + 15² - RS²] / [ 2(8.08)(15) ]
1/2 = [ 65.28 + 225 - RS²] / [ 242.4 ]
121.2 = 65.28 + 225 - RS²
121.2 = 290.28 - RS²
RS² = 290.28 - 121.2
RS² = 169.08
∴ RS = 13 km
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