Question

Which expressions can be used to find m∠ABC? Select two options. cos−1(StartFraction 9.8 Over 6.3 EndFraction) cos−1StartFraction 6.3 Over 9.8 EndFraction) cos−1(StartFraction 7.5 Over 9.8 EndFraction) sin−1(StartFraction 9.8 Over 7.5 EndFraction) sin−1(StartFraction 7.5 Over 9.8 EndFraction)

Answer 1

B.
`Cos ^(-1)`
`(6.3)/(9.8)`

E.
`Sin^(-1)`
`(7.5)/(9.8)`

Explanation:

The trigonometric functions are applied when given a side and one of the angles of a right angled triangle.

Sine θ =
`(opposite)/(hypotenuse)`

Cosine θ =
`(adjacent)/(hypotenuse)`

Tangent θ =
`(opposite)/(adjacent)`

Given that; hypotenuse = 9.8, opposite side = 7.5 and adjacent side = 6.3.

Then,

Sin θ =
`(7.5)/(9.8)`

⇒ θ =
`Sin^(-1)`
`(7.5)/(9.8)`

Also,

Cos θ =
`(6.3)/(9.8)`

⇒ θ =
`Cos ^(-1)`
`(6.3)/(9.8)`

So, the appropriate answers to the given questions are options B and E.