A hiker leaves her camp and walks 3.5 km in a direction of 55° south of west to the lake. after a short rest at the lake, she hikes 2.7 km in a direction of 16° east of south to the scenic overlook. what is the magnitude of the hiker's resultant displacement? round your answer to the nearest tenth

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Physics

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20 May, 17:42

A hiker leaves her camp and walks 3.5 km in a direction of 55° south of west to the lake. after a short rest at the lake, she hikes 2.7 km in a direction of 16° east of south to the scenic overlook. what is the magnitude of the hiker's resultant displacement? round your answer to the nearest tenth

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Greta Oneal · Answer 1

This can be solve by using a triangle, where the longest side of the triangle is the displacement of the hiker

First solve the opposite angle of the longest side which is:

C = 180 - 16 - (90 - 45)

C = 129 degrees

Then using the cosine law to solve the displacement

c^2 = a^2 + b^2 - 2ab (cos C)

c^2 = 3.5^2 + 2.7^2 - 2 (3.5) (2.7) cos (129)

c^2 = 31.43

c = 5.6 km