A truck travelled 1.5 kilometers up a ramp which is inclined to the horizontal at an angle of 58 degrees. Find the height at which the truck stopped giving the answer in meters to one decimal place.
So here we have the ground and we have a truck going up this ramp that is 1.5 kilometers. And it’s inclined to the horizontal, meaning the ground because the ground is horizontal, at an angle of 58 degrees. And it says to find the height at which the truck stopped giving the answer in meters. So we can let the height be 𝑥 meters. So essentially, we have this right triangle. So we can use trigonometry to solve for 𝑥. Based on our angle, 𝑥 would be the opposite side and the 1.5 would be the hypotenuse side because it’s the longest side and it’s the side across from the 90-degree angle.
Sometimes it’s helpful to use Soh Cah Toa to help us to remember sine, cosine, and tangent. Sine is equal to the opposite side divided by the hypotenuse side. Cosine is equal to the adjacent side divided by the hypotenuse side. And tangent is equal to the opposite side divided by the adjacent side. So here in our example, we’re looking at the opposite side and the hypotenuse side. So we need to use sine.
So the sine of our angle, the sine of 58 degrees is equal to 𝑥 over 1.5, the opposite side of the hypotenuse side. We can solve for 𝑥 by multiplying both sides by 1.5. So we get that 𝑥 is equal to 1.27. Now we multiplied by the 1.5, so we’re working with kilometers. Now it did say to round to one decimal place. So to decide whether or not to keep the two at two or raise it up to a three, we look at this seven. And since seven is larger than five, it will round the two up to a three. So since there are 1000 meters in one kilometer and we have 1.3 kilometers, we need to take 1.3 and move the decimal three places because we’re multiplying by a 1000. So the same as multiplying by a 1000, we will get 1300 or moving the decimal three places.
Therefore, the height at which the truck stopped would be 1300 meters.