Question

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

Answer 1

`\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}}`