Problem preview

G-SRT.11 Core M3-043-R08-V04

Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.

Find a resultant from non-right vector geometry

Problem

A route goes \(8~\text{km}\) north, then \(11~\text{km}\) at \(35°\) east of north, as shown. Find the resultant displacement and its direction east of north.

Answer choices

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Use the correct magnitude 18.1 km but report 35°-20.4°=14.6° as though it were measured east of north.

Add magnitudes and ignore the turn, reporting R=19 km due north.

Use a minus sign: R=√(8²+11²-2·8·11cos35°)=6.4 km, while still reporting 20.4° east of north.

R=√(8²+11²+2·8·11cos35°)=18.1 km, and direction=atan[(11sin35°)/(8+11cos35°)]=20.4° east of north.

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Curriculum context

Course: Math III
Standard: G-SRT.11
Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Objective: Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.
Problem type: Find a resultant from non-right vector geometry