The first triangle has a hypotenuse length of 12 and a 90 degree and 20 degree angle, how do you solve the triangle?

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Answer 1 · 2018-04-02T13:21:17

The two missing side lengths are 4.10 and 11.3 to three significant figures

#Sin theta= ("Opposite")/("Hypotenuse") #

#Cos theta= ("Adjacent")/("Hypotenuse") #

So if you want to find the side, opposite of your angle first, you use the formulas as mentioned above:

#Sin(20°) = x/12 #

#x = sin(20)*12 #

which if you type it into your calculator, gives 4.10 to three significant figures.

To find the last missing side (being the one adjacent to the 20° angle) you use the cosine rule

#Cos(20°) = x/12 #

#x = cos(20)*12#

which gives the value of 11.3 to 3sf.