If tan-3-4- find sin-

The correct option is B 3/5 Δ ABC is right angled at B, Given tan θ = 3/4. tan θ = AB/BC Let AB=3k and BC=4k Applying Pythagoras theorem, we have AB^2 + ...

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Byju's Answer

Standard IX

Mathematics

Trigonometric Ratio(sin,cos,tan)

If tanθ=3/4, ...

Question

If $t a n θ = \frac{3}{4}$ , find $s i n θ$ .

$\frac{3}{5}$

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$\frac{4}{5}$

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$\frac{5}{4}$

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$\frac{5}{3}$

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Solution

The correct option is A
$\frac{3}{5}$

$Δ A B C$ is right angled at B,
Given
$t a n θ = \frac{3}{4} .$

$t a n θ = \frac{A B}{B C}$

Let AB=3k and BC=4k

Applying Pythagoras theorem, we have

$A B^{2} + B C^{2} = A C^{2}$

$A C^{2} = (3 k)^{2} + (4 k)^{2}$

$A C^{2} = 25 k^{2}$

$A C = 5 k$

$⟹ A B : B C : A C = 3 : 4 : 5$

$⟹ s i n θ = \frac{A B}{A C} = \frac{3}{5}$

Suggest Corrections

If tan θ=34, find sin θ.

The correct option is A 35 ΔABC is right angled at B, Given tan θ=34. tan θ=ABBC Let AB=3k and BC=4k Applying Pythagoras theorem, we have AB2+BC2=AC2 AC2=(3k)2+(4k)2 AC2=25k2 AC=5k ⟹AB:BC:AC=3:4:5 ⟹sinθ=ABAC=35

If $t a n θ = \frac{3}{4}$ , find $s i n θ$ .