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

Answer 1

Aurora Ayala

#abs(AC)~~13.05#
#abs(AB)~~8.39#

If #/_B=90^@# and #/_C=40^@# #rarr /_A=50^@#

By the Law of Sines: #color(white)("XXX")abs(BC)/sin(A)=abs(AC)/sin(B)=abs(AB)/sin(C)#

#sin(A)=sin(50^@)~~0.766044# #sin(B)=sin(90^@)=1# #sin(C)=sin(40^@)~~0.642789#

#abs(AC)=abs(BC)/sin(A)*sin(B)~~10/0.766044*1~~13.0541#

#abs(AB)=abs(BC)/sin(A)*sin(C)~~13.0541*0.642789~~8.39100#

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Answer 2

Theodore Abad

The length of side AB is approximately 7.66 units, and the length of side AC is approximately 6.16 units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.