Understanding Trigonometric Functions: Solving for Length AD

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To find the length AD, the calculations using 8sin20 and 8cos70 initially appeared to yield different results. However, the discrepancy was due to the calculator being set to radians instead of degrees. Once corrected, both calculations align with the expected values. Additionally, it is noted that cos70 must be less than 0.5, confirming that 8cos70 cannot exceed 5. Understanding the correct mode for calculations is crucial in solving trigonometric problems accurately.
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I need to find the length AD. I thought that with the numbers given, and angle A worked out to being 70o 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.
 

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They don't give different values.
 
My calculator gives 8cos70 = 5.067 and 8sin20 = 7.304.
 
just realized it was in raidians mode. Whoops!
 
smulc said:
My calculator gives 8cos70 = 5.067 and 8sin20 = 7.304.

and you should realize (hopefully quickly) that if cos60o=1/2 then cos70o must be less than half, so there is no way 8cos70o > 5, and similarly with sin20o :wink:
 

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