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the submarine captain starts ascending at a constant angle of inclination of 20 degrees so that he can surface in 5000 feet so it looks like this is submarines right here and he he starts surfacing he starts ascending at an angle of 20 degrees so he starts going on 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 and kilo Pascal's is given by the equation the pressure in kilo Pascal's is approximately two point nine nine zero times your depth in in your depth and 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 drawn 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 kilo Pascal's at this starting depth right over here well how do you do that well if you're dealing with the right triangle and you know an angle and you know one of the sides you might remember that your your your trig your your definitions of your trig functions might come in handy and for just basic right triangles we always want to refer to so huh so katoa where so says that sine is equal to sine of an angle is equal to the ratio of the opposite side to the hypotenuse 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 all of if any of this looks foreign to 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 that that the hypotenuse is also right next to it so some people would call it adjacent we would call this the hypotenuse that is the longest side of the right triangle and then the jate 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 the tangent of 20 degrees is going to be equal to the ratio of the opposite side - 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 five thousand feet or if we want to solve for D we can just multiply both sides of this by five thousand multiply both sides by five thousand and we're gonna get D is equal to I'm just swapping sides here it's going to be equal to five thousand times the tangent of 20 degrees and then we could take whatever this value is in substituted down 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 do this 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 I could take 20 degrees and take the tangent of it so that's this right over here and then multiply it times 5000 so times 5 1 2 3 is going to be equal to this so that's my depth 1819 point 8 5 1 1 you know keeps going feet and now I can substitute into into this into this formula so let's see if I'm also take our D this is our D multiplied it by two point nine nine zero so let's multiply it by two point nine nine I could store zero there was not going to change the value is equal to that and then add 101.3 so plus 101 point three is equal to five thousand five hundred forty two point six five five zero zero and let's see I want to round to the nearest kilopascal this is this this P here is given in kilo Pascal's so it's going to be five thousand five hundred forty I'm gonna round up cuz I have a point six year five thousand five hundred and forty three so P is approximately five thousand five hundred and forty three five thousand five hundred and forty three kilo kilo pascals kilo Pascal's based on the information based on the information that they gave us but comma there by decimal a comma there you go