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Elina [12.6K]
3 years ago
10

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 ration

al denominator

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
8 0

Answer:

\tan(A) = \frac{3}{5}

Step-by-step 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) = \frac{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

(\sqrt{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) = \frac{Opposite}{Adjacent}

This gives:

\tan(A) = \frac{3}{5}

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