Question

Find the measurement of angle c. round to the nearest hundredth

Answer 1

The angle C measures 48.89°.

Explanation:

We use the Sine inverse trigonometric function to solve for C.

In a triangle the ratio of the side opposite to angle C, and the hypotenuse is given by the Sine function:

`sin(C)=(opposite)/(hypotenuse)`

and for our angle C, the opposite is 55 and the hypotenuse is 73; thus

`sin(C)=(opposite)/(hypotenuse)=(55)/(73)=0.7534`

Now the inverse sine function gives back the angle C, if the ratio
`(opposite)/(hypotenuse)` is known, that is

`\angle C=sin^(-1)((opposite)/(hypotenuse))`

We know that for angle C

`(opposite)/(hypotenuse)=0.7534`

therefore

`\angle C=sin^(-1)((opposite)/(hypotenuse))= sin^(-1)(0.7534})=48.89^o.`

`\boxed{\therefore \angle C=48.89^o.}`

Note that we did not use an equation when evaluating
`sin^(-1)(0.7534)` that is because there isn't any: you have just got to use a calculator or memorize some values for the inverse sine function.