### Video Transcript

A truck traveled 1.2 kilometers up a ramp that is inclined to the horizontal at an angle of 49 degrees, 18 minutes. Find the height at which the truck stopped, giving the answer in meters to one decimal place.

We can begin with a line that represents the horizontal. And then we have a ramp at an incline of 49 degrees, 18 minutes. After the truck has traveled the 1.2 kilometers up this ramp, what is the height at which the truck stopped?

Using our knowledge of right triangles, we can solve this problem. We’ll let the distance the truck traveled along the ramp be the hypotenuse. The incline of the ramp is our known angle, which makes our unknown value ℎ the opposite side length to that angle. To solve this problem, we’ll need one of our three trig ratios. We know that sin of 𝜃 is equal to the opposite side length over the hypotenuse. cos 𝜃 equals the adjacent side length over the hypotenuse. And tan 𝜃 equals the opposite side length over the adjacent side length. You might have memorized this using SOH CAH TOA.

The angle relationships we have are the opposite and the hypotenuse, which means we can use this sine relationship to solve the problem. For us, that is the sin of 49 degrees, 18 minutes is equal to ℎ over 1.2 kilometers. And this is where we should note that most of the time when we’re working with our calculators, it will be asking for degrees, not minutes. And that means we need to convert this 18 minutes to some fractional part of a degree. If one degree equals 60 minutes, then to convert 18 minutes into some kind of degree, we need to divide by 60, which is 0.3. And so we can rewrite our angle as sin of 49.3 degrees.

To solve for our missing ℎ-value, we multiply both sides of this equation by 1.2 kilometers. 1.2 kilometers times sin of 49.3 degrees is equal to 0.909761 continuing. Since we started in kilometers, this is a measure of the height of the truck in kilometers. We want to know the distance in meters to one decimal place. Since there are 1000 meters in every kilometer, we multiply this value by 1000. And that gives us 909.761 meters, rounded to one decimal place, is 909.8 meters. This means that after the truck had traveled 1.2 kilometers along the ramp, it was 909.8 meters vertically above the ground.