In ABC- if AB-6-3 cm- AC-12 cm and BC-6 cm- then find the measure - B-

[ ( AB ) ^ 2 =( 6√( 3 ) #160; ) ^ 2 =108; ( BC ) ^ 2 =( 6 ) ^ 2 =36; ( AC ) ^ 2 =( 12 ) ^ 2 =144; ( AC ) ^ 2 =( ...

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Byju's Answer

Standard IX

Mathematics

If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

In ABC, if ...

Question

In $△ A B C$ , if $A B = 6 \sqrt{3} c m, A C = 12 c m$ and $B C = 6 c m$ , then find the measure $∠ B$ .

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Solution

$\begin{matrix} {(A B)}^{2} = {(6 \sqrt{3})}^{2} = 108 {(B C)}^{2} = {(6)}^{2} = 36 {(A C)}^{2} = {(12)}^{2} = 144 {(A C)}^{2} = {(A B)}^{2} + {(B C)}^{2} \end{matrix}$
Therefore $Δ A B C$ is a right triangle with hypotenuse AC
Hence $∠ B = 90^{0}$

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Similar questions

Q. In

△ A B C, A B = 6 \sqrt{3} c m, A C = 12 c m

and

B C = 6 c m

. The

∠ B

is :

Q. Tick the correct answer and justify: In

△ A B C, A b = 6 \sqrt{3} c m, A C = 12 c m

and

B C = 6 c m

. The angle

B

is:

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC

Q. In

△ A B C, ∠ B = 90^{o}

. Find the sides of the triangle, if :

A B = (x - 3) c m, B C = (x + 4) c m

and

A C = (x + 6) c m

Q. In △ABC, AB =

6 \sqrt{3}

cm, AC = 12 cm and BC = 6 cm. Then ∠B is
(a) 45^o
(b) 60^o
(c) 90^o
(d) 120^o

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In △ABC, if AB=6√3 cm,AC=12 cm and BC=6 cm, then find the measure ∠B.

(AB)2=(6√3)2=108(BC)2=(6)2=36(AC)2=(12)2=144(AC)2=(AB)2+(BC)2Therefore ΔABC is a right triangle with hypotenuse ACHence ∠B=900

In $△ A B C$ , if $A B = 6 \sqrt{3} c m, A C = 12 c m$ and $B C = 6 c m$ , then find the measure $∠ B$ .

$\begin{matrix} {(A B)}^{2} = {(6 \sqrt{3})}^{2} = 108 {(B C)}^{2} = {(6)}^{2} = 36 {(A C)}^{2} = {(12)}^{2} = 144 {(A C)}^{2} = {(A B)}^{2} + {(B C)}^{2} \end{matrix}$
Therefore $Δ A B C$ is a right triangle with hypotenuse AC
Hence $∠ B = 90^{0}$