Problem

High School Sports. The equations shown in the fo…

Problem 83 Easy Difficulty

Offroading. The angle of approach indicates how steep of an incline a vehicle can drive up without damaging the front bumper. The angle of departure indicates a vehicle's ability to exit an incline without damaging the rear bumper. The angle of approach $a$ and the departure angle $d$ for an $\mathrm{H} 3$ Hummer are described by the system $\{ \left\begin{array}{l}{a+d=77} \\ {a=d+3}\end{array}$. Use substitution to \right. solve the system. (Each angle is measured in degrees.)
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Answer

Angle of approach: $40^{\circ} ;$ angle of departure: $37^{\circ}$

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 4

Systems of Linear Equations and Inequalities

Section 2

Solving Systems of Equations by Substitution

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Video Transcript

All right, so we're going to use a system of equations to solve the following problem. So they're saying that we can model complimentary angles is a system to solve it. So if we know what one angle is, we can find the other angle so important things to note that complimentary angles add up to 90 degrees. So x plus y would be 90 degrees now in the problem. They're telling us that one of the angles is Well, let's just say this is the other equation they've given us why is equal to X plus 46. Now, the problem with this right now is this is not set up in standard form for a system first system. Your variables have to be on the same side. So this guy, I'd actually have to write it as why minus X equals 46 to use it as a system variables on one side, constant on the other side. So when I go to set up my matrix, I also have to be careful because not necessarily the same order as well. So we're gonna just label this one to make our life a little bit easier. Equation one equation, too. So for my first equation, I have one x one y and they add up to 90. In my second equation, I have negative one x one y, and that adds up to 46. So the orders actually backwards. It's not one negative one. It's negative 11 Now I could go about solving it. So I'm gonna take my first row, and I'm going to add it to my second row to cancel out that number. The negative one. So 11 90 one native one plus 101 plus one is 2 46 plus 90 is 100 and 36. Now I'm going to take half of my second road to try to get rid of that. Too side much of 11 90 01 and 100 half of 136 is 68 and then, lastly, I'm going to take my second row and subtract it from my first row. That leaves me with 10 on 98 minus 68 or 90 minus 68 which is 22 then 01 60 eight. So that tells us that are X is 22 for angle are why 68 four angles? Those add up to 90 So our solution to these complimentary angles would be 22 and 68.

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