Following the symbols in the image:
Assuming 15cm corresponds to a (the line adjacent to the angle), then you need to use the cosine formula
cos(ø) = a/h
cos(31º) = 15cm/h
h*cos(31º) = (15cm/h) * h
h*cos(31º) = 15cm * 1
h*cos(31º)/cos(31º) = 15cm/cos(31º)
h*1 = 15cm/cos(31º)
h = 16.398
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The length of the third side is 20 cm
We don't know whether the 15cm happens to be the hypotenuse (longest side) of the right triangle. It makes a big difference. -- If the 15cm is the longest side, then the third side is 7.483 cm. (rounded) -- If the 13cm and the 15cm are the "legs", then the hypotenuse is 19.849 cm. (rounded)
Using Pythagoras' theorem: 15 times the square root of 2 cm in length
12 cm
Use Pythagoras' Theorem : In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let H be the hypotenuse then :- H2 = 152 + 82 = 225 + 64 = 289 Then H = √289 = 17cm