(Modeling) Grade Resistance Solve each problem. See Example 3.

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Question

(Modeling) Grade Resistance Solve each problem. See Example 3.

A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the nearest tenth of a degree.

Accepted Answer

Welcome back. Everyone in this problem. The great resistance of a £580 motorcycle climbing a hill is £29 determine the grid angle to the nearest degree. For our answer choices. A is four degrees. B is three degrees C is two degrees and D is one degree. Now, what are we trying to figure out here? We want to figure out the great resistance. And if we were to just do a sketch of our problem, we're saying that we have a motorcycle, OK. That's traveling up a hill, are climbing up a hill and it's climbing the hill at an angle. The grade resistance is the force acting on our motorcycle. So recall that the grade resistance formula is F equals W multiplied by the sign of theta where F is our grade resistance and W is the weight of the automobile. Let's look at our problem. We have the weight of our automobile and we have the great resistance, but we're trying to figure out the great angle. So since our great resistance F equals £29 and the weight of our automobile is £580 the weight of our motorcycle, then we can substitute these values of F and W to solve for the value of theta. Because now this tells us that our grade resistance 29 points equals our weight 580 points multiplied by the sign of our grade angle. Now, if we're going to solve, let's do some transposing here. First, let's divide both sides by 580. No, on the, I'm going to leave it as is on the left hand side and on the right hand side, I have 5 80 Cancers 5 80 that just leaves me with a sign of the. So the sign of theater equals 29 divided by 580. Now, am I going to figure out the value of theater? Well, again, recall that for the, if we have sine theta being equal to a value a ratio, then our angle would be equal to the inverse sign of that value ratio. So in this case that tells us then that theta equals the inverse sign of 29 divided by 580. So we can put this in our to get an exact value. Now make sure that your calculator is in degree mode. And when you find the inverse sign of 29 divided by 580 you should get 2.8659839826. And for some calculators, it continues on, but we're not interested in all those digits because remember we want it to the nearest degree. So to get it to the nearest degree, the, if we look at the degree, the digit beside the degree is the 10th place, which is greater than five. So that means we're going to round up. So to the nearest degree, theta equals three degrees. When we look back on our answer choices, that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

(Modeling) Grade Resistance Solve each problem. See Example 3. A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the nearest tenth of a degree.

Key Concepts

Grade Resistance

Trigonometric Functions

Right Triangle Relationships

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