In right ∆ABC, m B = 90°, m C = 40°, and BC = 10. What are the other two side lengths of the triangle?

Question

anonymous · Answer

please help

anonymous · Answer

lets try another picture

anonymous · Answer

|dw:1404101442456:dw|

anonymous · Answer

since this one is a right triangle it is much easier

anonymous · Answer

we need to label the sides also 
usually use lower case ones opposite the upper case angles |dw:1404101589053:dw|

anonymous · Answer

then for example 
$$\tan(40)=\frac{c}{10}$$ so$$c=10\tan(40)$$

anonymous · Answer

how would you find the answer

anonymous · Answer

you have to use a calculator

anonymous · Answer

well i haven't actually used a calculator since about 2004 i would use this http://www.wolframalpha.com/input/?i=10tan%2840%29

anonymous · Answer

you have lots of choices to find $b$ 
you good from there?

triciaal · Answer

another option is to find b first knowing Sin 90 =1 and using 
10/sin 50 = b/sin 90 = c/sin 40
b = 10/sin 50 =13
pythagorean theorem  c^2 =13^2 -10^2 =69  so c = rt of 69