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HOWW DO I DO THIS????
WEIRD EXACT TRIG QUESTION (cannot use a calculator)

HOWW DO I DO THIS???? WEIRD EXACT TRIG QUESTION (cannot use a calculator)-example-1
User Ashish Sarkar
by
2.8k points

1 Answer

6 votes
6 votes

Answer:


\huge{\red{\angle ABC = \boxed{30}\degree}}

Explanation:


  • \sin \angle ABC =(p)/(30)......(1) (Given)

  • In
    \triangle ABC, sin ratio of
    \angle ABC can be given as:


  • \sin \angle ABC =(AC)/(AB)


  • \implies \sin \angle ABC =(2p+10)/(80)......(2)

  • From equations (1) and (2), we find:


  • (p)/(30)=(2p+10)/(80)


  • \implies 80(p)=30(2p+10)


  • \implies 80p=60p+300


  • \implies 80p-60p=300


  • \implies 20p=300


  • \implies p=(300)/(20)


  • \implies p=15


  • \implies \sin \angle ABC =(15)/(30)


  • \implies \sin \angle ABC =(1)/(2)


  • \implies \sin \angle ABC =\sin 30\degree\:\:\:\:(\because \sin 30\degree=(1)/(2))


  • \implies \huge{\red{\angle ABC = \boxed{30}\degree}}
User Najathi
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