The value of tan - in given ABC in terms of a- b and c is

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Byju's Answer

Standard IX

Mathematics

Trigonometric Identities

The value of ...

Question

The value of $t a n θ$ in given $△$ ABC in terms of a, b and c is

\frac{b}{c}

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\frac{b}{a}

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\frac{a}{c}

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Solution

The correct option is C $\frac{a}{c}$
$We know that t a n θ = \frac{Opposite side}{Adjacent Side}$

For the angle $θ$ the opposite side is BC and its length is $a$ . The adjacent side is AB, and its length is $c$

$∴ t a n θ = \frac{B C}{A B} = \frac{a}{c}$

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In the figure given above, what is the value of

t a n θ

in terms of a,b and c?

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Q. In a triangle ABC we define

x = t a n \frac{B - C}{2} t a n \frac{A}{2}

y = t a n \frac{C - A}{2} t a n \frac{B}{2}

and

z = t a n \frac{A - B}{2} t a n \frac{C}{2}

then the value of

x + y + z

(in terms of x, y, z) is

In a triangle $A B C$ we define
$x = t a n \frac{B - C}{2} t a n \frac{A}{2}, y = t a n \frac{C - A}{2} t a n \frac{B}{2}$ and $z = t a n \frac{A B}{2} t a n \frac{C}{2}$
Then the value of $x + y + z$ (in terms of $x, y, z$ ) is

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The value of tan θ in given △ ABC in terms of a, b and c is

The correct option is C ac We know that tan θ=Opposite sideAdjacent Side For the angle θ the opposite side is BC and its length is a. The adjacent side is AB, and its length is c ∴tan θ=BCAB=ac

The value of $t a n θ$ in given $△$ ABC in terms of a, b and c is

The correct option is C $\frac{a}{c}$
$We know that t a n θ = \frac{Opposite side}{Adjacent Side}$

For the angle $θ$ the opposite side is BC and its length is $a$ . The adjacent side is AB, and its length is $c$

$∴ t a n θ = \frac{B C}{A B} = \frac{a}{c}$