Suppose that m /_BCA=70^@, and x=33 cm and y = 47 cm. What is the degree measure of /_ABC?01510101651.png

Reggie 2020-12-27 Answered

Suppose that mBCA=70, and x=33 cm and y=47 cm. What is the degree measure of ABC?
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Expert Answer

Brittany Patton
Answered 2020-12-28 Author has 100 answers
AB=AC2+BC2(2ACBCcosBCA)
AB=472+332(24733cos70)
AB=2237.05
AB=47.29
Using the cosine law,
ABC=cos1(BC2+AB2AC22BCAB)
ABC=cos1(332+47.29247223347.29)
ABC=cos1(0.3576)
ABC=cos1=69.04
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Answered 2021-12-16

Step 1

Given that

x=33 cm, y=47 cm

mBCA=70

ABC=?

using cosine Rules

cosC=(AC)2+(BC)2(AB)22(AC)(BC)

cos70=(47)2+(33)2(AB)22×47×33

0.3420=3298(AB)23102

AB=47.30 cm

Using sine rule

sinABC47=sinBCA47.30

sinABC=4747.30×sin70

sinABC=0.9337

ABC68.24

ABC68.72

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