Question

A pair of runners leaves the same starting point at the same time. The angle between the runners paths is 85 degrees. They stop after running for 30 seconds and are 180 meters apart. One runner ran 130 meters. How far did the other run? Step by step explanation..Please.Thanks

Answer 1

136.34 m to the nearest hundredth.

Explanation:

The runners paths and the distance between them after 30 second form a triangle.

The side opposite the 85 degree angle is 180 m and one of the other sides is 130 m.

We need to find the third side.

We can use the Cosine Rule to do this:

If the third side is x m then:

180^2 = 130^2 + x^2 - 2*130x cos 85

180^2 = 130^2 + x^2 - 260 * x * 0.08716

180^2 = 130^2 + x^2 - 22.6616 x

x^2 - 22.6616 x - 15500 = 0

x = [22.6616 +/- sqrt ((-22.6616)^2 - 4 * -15500) ] / 2

x= 136.34 m.

Answer 2

136.4

Explanation:

Firstly ,check the following picture

according to the law of sine:

`(130)/(sin(B)) =(180)/(sin(85)\\) \\then\\sin(B)=(130*sin(85))/(180) \\\\then\\\\B = sin^(-1)(0.719473948622)=46\\\\A= 180-(85+46) = 49\\\\\\(180)/(sin(85)) =(c)/(sin(49)) \\then\\\\c=(180*sin(49))/(sin(85)) =136.4`