Question

given sin A =3/-/34 and that angle S is in quadrant 1, find the exact value of tan A in simplest radical form using a rational denominator

Answer 1

`\tan(A) = (3)/(5)`

Explanation:

Given

`\sin(A) = \frac{3}{\sqrt {34}}`

`0 \le A \le 90` --- First Quadrant

Required

Find tan(A)

The sin of an angle is:

`\tan(A) = (Opposite)/(Hypotenuse)`

and

`\sin(A) = \frac{3}{\sqrt {34}}`

By comparison:

`Opposite = 3`

`Hypotenuse = \sqrt{34`

So, the Adjacent is:

`Hypotenuse^2 = Adjacent^2 + Opposite^2`

`(√(34))^2 = Adjacent^2 + 3^2`

`34 = Adjacent^2 + 9`

Collect like terms

`Adjacent^2 =34 - 9`

`Adjacent^2 =25`

Take square roots

`Adjacent =\sqrt{25`

`Adjacent =5`

The tangent of an angle is:

`\tan(A) = (Opposite)/(Adjacent)`

This gives:

`\tan(A) = (3)/(5)`