In a triangle ABC right angled at B- ACB-If tan - - 3-4 -then find sin -

Given, triangle ABC is right angled at B, Also, tan θ = 3/4 tan θ = AB/BC Let AB = 3k and BC = 4k Applying Pythagoras theorem, we get, nbsp;AB^2 + BC^2 ...

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Standard X

Mathematics

Trigonometric Ratios of a Right Triangle

In a triangle...

Question

In a triangle ABC right angled at B,
$∠ A C B = θ .$
$If t a n θ = \frac{3}{4}, then find s i n θ$ .

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Solution

Given, triangle ABC is right angled at B,

$Also, t a n θ = \frac{3}{4}$

$t a n θ = \frac{A B}{B C}$

Let AB = 3k and BC = 4k

Applying Pythagoras theorem, we get,

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

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

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

$A C = 5 k$

$\Rightarrow A B : B C : A C = 3 : 4 : 5$

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

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In a triangle ABC right angled at B, ∠ACB=θ. If tan θ=34,then find sin θ.

Given, triangle ABC is right angled at B, Also, tan θ=34 tan θ=ABBC Let AB = 3k and BC = 4k Applying Pythagoras theorem, we get, AB2+BC2=AC2 AC2=(3k)2+(4k)2 AC2=25k2 AC=5k ⇒AB:BC:AC=3:4:5 ⇒sinθ=ABAC=35

In a triangle ABC right angled at B,
$∠ A C B = θ .$
$If t a n θ = \frac{3}{4}, then find s i n θ$ .