Understanding Trigonometric Functions: Solving for Length AD

[smulc]

I need to find the length AD. I thought that with the numbers given, and angle A worked out to being 70^o there would be two different ways of working length AD out. I thought 8sin20 and 8cos70 would both be acceptable ways of calculating the length but they give different values. Where have I gone wrong?

Thanks.

 

[Millennial]

They don't give different values.

 

[smulc]

My calculator gives 8cos70 = 5.067 and 8sin20 = 7.304.

 

[smulc]

just realized it was in raidians mode. Whoops!

 

[Mentallic]

My calculator gives 8cos70 = 5.067 and 8sin20 = 7.304.

and you should realize (hopefully quickly) that if cos60^o=1/2 then cos70^o must be less than half, so there is no way 8cos70^o > 5, and similarly with sin20^o