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# Right triangle word problem

CCSS.Math:

## Video transcript

a tiny but horrible alien is standing at the top of the Eiffel Tower so this were the tiny but horrible alien is which is 324 meters tall and they label that the height of the Eiffel Tower and threatening to destroy the city of Paris a men in black or I guess aim or a men in black age and I was about to station maybe should be a man in black a men in black agent is standing at ground level 54 meters across the eiffel square so 54 meters from I guess you could say the center of the base of the Eiffel Tower aiming his laser gun at the alien so this is him aiming the laser gun at what angle should the agent shoot his laser gun round your answer if necessary to two decimal places so if we construct a right triangle here and we can so the height of this right triangle is 324 324 meters this width right over here is 54 meters it is a right triangle what they're really asking us is what is the angle what is this angle what is this angle right over here and they've given us two pieces of information they gave us the side that is opposite the angle and they've given us the side that is adjacent to the angle so what trig function deals with opposite and adjacent and to remind ourselves we can write like I always like to do Sokka Toa and these are really by definition so you just kinda have to know this and sohcahtoa helps us sine is opposite over hypotenuse cosine is adjacent over hypotenuse tangent is opposite over adjacent so we can say that the tangent we can write that the tangent of theta the tangent of theta is equal to the length of the opposite side 324 meters 324 meters over the length of the adjacent side over 50 over 54 meters now you might say well okay that's fine no so what what angle gives the when I take its tangent gives me 324 or 54 well for this it will probably be useful to use a calculator and the way we use a calculator is we would use the inverse tan function so we would we could rewrite this as we're going to take the inverse tangent and sometimes it's written as tangent kind of this negative 1 superscript so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324 324 over 54 over 54 and just to be clear what is this inverse tangent this is literally says what is this will return what is the angle that when I take the tangent of it gives me 324 over 54 this says what is the 10th what is the angle that when I take the tangent of it gives me tangent of theta so this right over here is just going to this just simplifies to theta theta is the angle that when you get the tangent of it gets you tangent of theta and so we get theta is equal to tangent inverse tangent of 324 324 over 54 once again this inverse tangent thing you might find confusing but all this is saying is over here is saying tangent of some angle is 324 or 54 this is just saying is my angle is whatever angle I need so that when I take the tangent of it I get 324 over 54 is how we will solve for theta so let's get our calculator out and let's say that we want our answer in degrees and actually they should well I'm just going to assume that they they want our answer in degrees so let me make sure my calculator is actually in degree mode so I'll go to the second mode right over here and actually it's in Radian mode right now so let me make sure I'm in degree mode to get my answer in degrees now let me exit out of here and let me just type in the inverse tangent so it's in this yellow color right inverse tangent of 324 divided by 54 is going to be 80 point and they told us to round to two decimal places 80 point five four degrees so theta is equal to 80 point five four degrees that the angle at which you should shoot the gun to to help defeat this horrible alien