Question

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

Answer 1

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

Explanation:

`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.