In the right angled triangle #ABC#, right angled at #C#, hypotenuse #AB# is #3.1 cm# and side BC is #2.7 cm#. Find its remaining side and angles (length to nearest tenth and angles to nearest degrees)?

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Answer 1 · 2016-03-14T06:58:35

#AB=3.1 cm#, #BC=2.7 cm# and #CA=1.5 cm# and

angles #A=61^o#, #B=29^o# and #C=90^o#.

In the right angled triangle #ABC#, right angled at #C#, hypotenuse #AB# is #3.1 cm# and side BC is #2.7 cm#.

Hence side AC is #sqrt(3.1^2-2.7^2)=sqrt(9.61-7.29)=sqrt2.32=1.523#

It is obvious that angle #C=90^o#

Also as #cosB=(BC)/(AB)=2.7/3.1=0.871#, angle #B=29.425^o#

Hence angle #A=(90-29.425)=60.575^o#

Hence, length to nearest tenth and angles to nearest degrees are

#AB=3.1 cm#, #BC=2.7 cm# and #CA=1.5 cm# and

angles #A=61^o#, #B=29^o# and #c=90^o#.