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Current time:0:00Total duration:5:33

Right triangle word problems — Harder example

Video transcript

- [Instructor] The submarine captain starts ascending at a constant angle of inclination of 20 degrees so that he can surface in 5,000 feet. So it looks like this is the submarine right here and he starts surfacing, he starts ascending, at an angle of 20 degrees. He's just going in that direction so this is our angle of 20 degrees. And he wants to surface. So I guess this is the surface, right over here, of the water. He wants to surface after traveling 5,000 feet in the horizontal direction. Changes in pressure are very important in submarine travel, and the pressure in kilopascals is given by the equation the pressure in kilopascals is approximately 2.990 times your depth. And your depth in, I guess it's going to be feet, plus 101.3. What is the current pressure, P, on the submarine at depth d? Round your answer to the nearest kilopascal. All right, so if we can figure out and they've kind of draw a nice right triangle for us where this angle right over here is 20 degrees, and so if we can use a little bit of mathematics to figure out what d is then we can substitute d into this formula right over here and figure out the pressure in terms of kilopascals at this starting depth right over here. Well how do you do that? Well if you're dealing with a right triangle and you know an angle and you know one of the sides, you might remember that your trig, you definitions of your trig functions might come in handy. And for just basic right triangles you always want to refer to soh cah toa where soh says that sine is equal to, sine of an angle is equal to the ratio of the opposite side to the hypothenuse, cosine of an angle is equal to the ratio of the adjacent to the hypotenuse, and tangent of an angle is equal to the ratio of the opposite side to the adjacent side. So we have our angle here. Now what sides are we trying to deal with? We're trying to deal with this side right over here, is the opposite side. And if any of this looks foreign to you I encourage you to review the basic trigonometry on Khan Academy. And then this side right over here, it's not the hypotenuse, it's the adjacent side. You could argue that the hypotenuse is also right next to it so some people would call it adjacent, but we could call this the hypotenuse. That is the longest side of the right triangle. And then the adjacent side that is not the hypotenuse, that's the one that we call the adjacent side. So this is the adjacent side. So we're gonna be dealing with the opposite and the adjacent. So which trig function comes into play here? Well tangent deals with the opposite and the adjacent. So we know that the tangent of 20 degrees is going to be equal to the ratio of the opposite side to, or the length of the opposite side to the length of the adjacent side. So it's going to be d feet over five over 5,000 feet. Or if we want to solve for d we could just multiply both sides of this by 5,000. Multiply both sides by 5,000 and we're gonna get d is equal to, and I'm just swapping sides here, is going to be equal to 5,000 times the tangent of 20 degrees. And then we could take whatever this values is and substitute it down here and round to the nearest kilopascal. Well tangent of 20 degrees, we're gonna need a calculator for that and luckily we have one. Now when you use your calculator you want to be very careful that you are in the correct mode. So you want to be very careful that you are in degree mode. Depending on your calculator there's different ways of going between degree and radian mode and I encourage you to get familiar with that. That's just going to be useful for you, potentially on the SAT but for sure when you're in trigonometry class. But I'm in degree mode here. So I could take 20 degrees and take the tangent of it. So that's this right over here. And then multiply it times 5,000. So times five, one, two, three, is going to be equal to this. So that's my depth, 1,819.85118, it keeps going, feet. And now I can substitute into this formula. So let's see, if I take our d, this is our d, multiply it by 2.990. So let's multiply it by 2.99, well I could throw a zero there but it's not gonna change the value. Is equal to that, and then add 101.3. So plus 101.3, is equal to 5,542.65500. And let's see, I want to round to the nearest kilopascal. And this P here is given in kilopascals. So it's gonna be 5,540. I'm gonna round up 'cause I have a .6 here. 5,543, so P is approximately 5,543. 5,543 kilopascals. Kilopascals, based on the information, based on the information that they gave us. Put a comma there not a decimal. A comma, there you go!