Biking, triangle

Question

A biker pedaled up a slope of 6 degrees for 150 meters and then another 100 meters at a slope of 9 degrees. 

a. How far did the biker travel in a horizontal distance?

b. How far did the biker climb vertically? 

Answer 1

This is the sum of the sides of two triangles. You have been given the hypotenuse and angle, and need to use sine and cosine to arrive at the answers.

 

So, for the first question, the length of an adjacent side of a right triangle can be found using cos(theta) = a/h. You know the angle and the hypotenuse, so the solution is a = cos(6) x 150 m. Do the same for the second leg of the ride and sum the answers to find the total horizontal distance covered.

 

The second question is addressed in a similar way, but in this case you are solving for the opposite, so use sine instead.