Question

Please help! Geometry.

Answer 1

These are right triangles that will use either sin, cos, or tan, depending upon what you have to work with in regards to the reference angle. The first one has a reference angle of 51 with y being the side opposite it and 12 being the hypotenuse. The sin identity uses the side opposite over the hypotenuse as its formula:

`sin(51)= (y)/(12)`
and 12 sin(51) = y and y = 9.325
The second one has the reference angle as the unknown. You could use any of the identities here because you have all the sides of the triangle, but I will use sin again:

`sin \beta = (12)/(13)`
and
`sin \beta =.9230769`
and
`sin ^(-1)(.9230769)=67.38`
The next one has a referece angle of 13 with 24 being the side adjacent to it and the unknown being the side across from it. You will use the tangent identity here:

`tan(13)= (x)/(24)`
and 24 tan(13) = x so x = 5.540
The last one has a reference angle of 20 with the hypotenuse as the unknown x, and the side across from it as 10. Use the sin identity again:

`sin(20)= (10)/(x)` and

`x sin(20)=10` and

`x= (10)/(sin(20))` with x = 29.238
Everything is in regards to the reference angle; you HAVE to be able to identify the reference angle and then how the given sides are related to it.