Trignometry help please?

Okay. So they give us the time it takes to go up the hill and down the hill, but not the distance. Finding the distance will be our first step.

We can do this using the fact that we have time and speed. Speed x time = distance. This will give us the uphill side of the triangle. Remember that time happens to be in minutes and distance is in hours, so we have to convert our time to hours using 1h=60 minutes.

I saw from your picture that you've already started trying to use law of sines, which means you're on the right track.

Okay. So since we figure out the length of the uphill side of the triangle using time x speed, we can figure out the length of the downhill side of the triangle using the law of signs.

So remember the law of sines is,

sin(angle1)/length of side opposite angle 1 = sin(angle2)/side opposite angle2

And remember, we can also invert them and put sin on bottom and length on top, it doesn't matter, as long as we write it the same way on both sides of the equation.

So after we figure out the length aka distance of the downhill side of the triangle, we can use time x speed = distance to solve for time, remembering again that this formula will give us time in hours and we'll need to convert it to minutes.

Hope this helps.

23km/h x 0.25 hours= 5.75km

USE sine LAW

A/(sin 7.2degree) = 5.75/ ( sin 8.1degree)

A= 5.1147 km

5.1147 km / (31 km/hours) = 0.165 hours = 9.9 minutes

about 10 minutes