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If theta is an acute angle for which tan...

If `theta` is an acute angle for which `tan^(2)theta = 6 tan theta - 9`, what is the degree measure of `theta` ?

A

`51.3`

B

`60.0`

C

`71.6`

D

`79.7`

Text Solution

Verified by Experts

The correct Answer is:
C
This is just a quadratic equation where the unknown is `tan theta` :
`tan^(2)theta = 6 tan theta - 9`
`tan^(2)-6 tan theta + 9 = 0`
`(tan theta - 3)^(2)=0`
`tan theta = 3`
`theta` = arctan (3)
`~~71.6^(@)`
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