How do you solve the right triangle given A=52 degrees and B=8.4?

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Answer 1 · 2018-07-27T19:15:50

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The sum of other two acute angles in a right #\triangle ABC# is #90^\circ#

#\angle A+\angle C=90^\circ#

#\angle C=90^\circ-\angle A#

#=90^\circ-52^\circ#

#=38^\circ#

Given that hypotenuse #B# of right #\triangle ABC# is #8.4#

Now, using sine rule in right #\triangle ABC#

#\frac{A}{\sin \angle A}=\frac{B}{\sin \angle B}=\frac{C}{\sin \angle C}#

#\frac{A}{\sin 52^\circ}=\frac{8.4}{\sin 90^\circ}=\frac{C}{\sin 38^\circ}#

#A=8.4\sin52^\circ=6.619#

#C=8.4\sin38^\circ=5.171#