Question

As the figure shows Elton runs 500 m to point b first then he turns 100 degrees and runs another 350 m to point c how far is the distance from point a to c

Answer 1

658.24 m

Explanation:

The figure makes a triangle with vertices abc.

Where ab = 500 m

bc = 350 m

The angle abc = 100°

Using the cosine rule we can find the distance ac.

ac² = 500²+350² - 2×500×350×cos100°

= 372,500 - -60,776.86

= 433,276.86

ac = √433,276.86

= 658.24 m

Answer 2

658.24 m

Explanation:

Let A be the point from where Elton started. Connect points A and C, you get triangle ABC with AB=500 m, BC=350 m and m∠B=100°. Use the cosine rule to determine the length of the segment AC:

`AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot \cos \angle B,\\ \\AC^2=500^2+350^2-2\cdot 500\cdot 350\cdot \cos 100^(\circ),\\ \\AC^2=250000+122500-350000\cdot (-0.174),\\ \\AC^2\approx 433276.8622,\\ \\ AC\approx 658.24\ m.`