Question

Solve the right triangle. Round decimal answers to the nearest tenth.12AB=m/Am/B

Answer 1

Given the shown triangle

Using the pithagorean theorem

`AB^2=9^2+12^2`
`AB=√(81+144)`
`AB=15`

AB=15

Using law of sines

`(a)/(sin(A))=(b)/(Sin(B))=(c)/(sin(C))`
`(12)/(sin(A))=(9)/(Sin(B))=(15)/(sin(90))`

Solving for A

`(12)/(Sin(A))=(15)/(sin(90))`
`(12)/(15)=Sin(A)`
`A=ArcSin((4)/(5))`
`A=53.13`

A=53.13°

Solving for B

`(9)/(S\imaginaryI n(B))=(15)/(s\imaginaryI n(90))`
`(9)/(15)=Sin(B)`
`B=ArcSin((3)/(5))`
`B=36.87`

B=36.87°