Question 401704: 1. If one leg of a right triangle is 18 and the and the angle adjacent to it is 30 degrees, find the other sides. (please show all work)
2. One side of a right triangle is 8 and the hypotenuse is 27. Find the 3 unknown parts of the triangle. (show all work. Explain how you did each step)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 1. If one leg of a right triangle is 18 and the and the angle adjacent to it is 30 degrees, find the other sides. (please show all work)
2. One side of a right triangle is 8 and the hypotenuse is 27. Find the 3 unknown parts of the triangle. (show all work. Explain how you did each step)
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1.Let's start by drawing a right triangle with sides a, b & c and opposing angles A, B & C, with c being the hypotenuse and a the side adjacent to the 30 deg angle.
Cos 30 deg =adjacent/hypotenuse=18/c=sqrt(3)/2
the last two terms give you an equation,
18/c=sqrt(3)/2
c=18/sqrt(3)/2
c=20.78
you can use the sin or tan function to find the third side(b), but it is known that the side opposite the 30 deg angle is equal to 1/2 the hypotenuse b=20.78/2=10.39
ans: the other two sides are 20.78 (hypotenuse) and 10.39(side b)
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2.We can designate the side of length 8 to be the side opposite the angle A we will find first.
sin A=opposite/hypotenuse=8/27
What this says here is that we must find an angle whose sin value=8/27.To do this, we must use the inverse functions of the calculator. Instead of entering the angle to find the value of the trig function, you will be entering the value of the function to get the angle. In this case, my calculator gave angle A to be
17.24 deg. The other angle would then be 90-A=90-17.24=72.76 deg. The third side could be found by using tht pythagorean theorem or the cos function of the 17.24 deg angle found.
cos 17.24=adjacent side/hypotenuse
adjacent side=cos 17.24*27=25.78
ans: The 3 parts of the triange found are: the angles 17.24 deg, and 72.6 deg and the third side, 25.78.
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