English, asked by chayapatil2626, 6 hours ago

in triangle ABC Ab=6√3cm,Ac=12cm,bc=6cm. find measure of angle A​

Answers

Answered by KnightLyfe
79

Question:

In triangle ABC AB=\mathsf{6\sqrt{3}}cm , AC=12cm, BC=6cm. find measure of angle A.

Given:

AB=\mathsf{6\sqrt{3} cm}

AC=12 cm

BC=6 cm

To Find:

Measure of \angle{A}

Solution:

Here,

\dashrightarrow\mathsf{{AB}^{2}+{BC}^{2}={(6\sqrt{3)}}^{2}+{(6)}^{2}} \: \: —(1)

We know,

\mathsf{{AC}^{2}={12}^{2}=144\: {cm}^{2}} \: \: —(2)

From (1) & (2),

\mathsf{AB}^{2}+{BC}^{2}={AC}^{2}

We also know, that AB²+BC²=AC² is Pythagoras theorem that implies on right angled Triangle, that means ∆ABC is right angled Triangle. So,

\implies\angle{B}

Now,

\dashrightarrow\mathsf{tanA=\large\frac{BC}{AB}}

\dashrightarrow\mathsf{tanA=\large\frac{6}{6\sqrt{3}}}

\dashrightarrow\mathsf{tanA=\large\frac{1}{\sqrt{3}}cm}

We know that, {tan30}{o}=\frac{1}{\sqrt{3}} . So,

\mathsf{\angle{A}={30}^{o}}

Hence, the measure of \angle{A} is 30°

___________________________________________

More to Know:

Trignometric Ratios -:

>\mathsf{sin\theta=\large\frac{perpendicular}{Hypotenuse}}

>\mathsf{cos\theta=\large\frac{Base}{Hypotenuse}}

>\mathsf{tan\theta=\large\frac{Perpendicular}{Base}}

>\mathsf{cosec\theta=\large\frac{Hypotenuse}{Perpendicular}}

>\mathsf{sec\theta=\large\frac{Hypotenuse}{Base}}

>\mathsf{cot\theta=\large\frac{Base}{Perpendicular}}

___________________________________________

Attachments:
Answered by Anonymous
18

GivEn:

  • AB = 6√3cm
  • AC = 12 cm
  • BC = 6 cm

To find:

  • The measure of angle A?

Solution:

• Let's consider ABC is a triangle.

Where,

  • Hypotenuse = 12 m = AC
  • Base = 6√3 cm = AB
  • Perpendicular = 6 cm = BC

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, By using Pythagoras Theorem,

→ (Hypotenuse)² = (Perpendicular)² + (Base

→ (12)² = (6)² + (6√3)²

→ 144 = 36 + 108

→ 144 = 144

∴ Hence, It is a right angled triangle.

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Let's find angle A,

Tan A = per/base

→ Tan A = 6/6√3

By cancelling 6,

→ Tan A = 1/√3

→ Tan A = 30°

∴ Hence, The measure of angle A = 30°.

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

More to know:

Trigonometric Identities:

  • sin²θ + cos²θ = 1
  • sec²θ - tan²θ = 1
  • csc²θ - cot²θ = 1

Trigonometric relations:

  • sinθ = 1/cscθ
  • cosθ = 1 /secθ
  • tanθ = 1/cotθ
  • tanθ = sinθ/cosθ
  • cotθ = cosθ/sinθ

Trigonometric ratios:

  • sinθ = opp/hyp
  • cosθ = adj/hyp
  • tanθ = opp/adj
  • cotθ = adj/opp
  • cscθ = hyp/opp
  • secθ = hyp/adj
Attachments:
Similar questions