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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Trigonometric Ratios of a Right Triangle

In a triangle...

Question

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

Open in App

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,

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

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

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

$A C = 5 k$

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

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

Suggest Corrections

Similar questions

Q. In a triangle ABC right angled at B,

∠ A C B = θ .

If t a n θ = \frac{5}{12}

then find the value of \frac{(1 + c o s θ) \times (1 - s i n θ)}{(1 + s i n θ) \times (1 - c o s θ)} .

If s i n θ = \frac{4}{5} and c o s θ = \frac{3}{5}, then find t a n θ .

Q. 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

Q. In a

△ A B C,

the angles

A

and

B

are two different values of

θ

satisfying

\sqrt{3} cos θ + sin θ = k, | k | < 2.

The triangle:

A B C

is a right-angled triangle, right-angled at

B

/. Given that

∠ A C B = θ

, side

A B = 2

units and side

B C = 1 u n i t

, find the value of

{sin}^{2} θ + {tan}^{2} θ

Join BYJU'S Learning Program

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,
$∠ A C B = θ .$
$If t a n θ = \frac{3}{4}, then find s i n θ$ .