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In a right angled ABC. m ABC =90^o, m=30^o. If BC=9 cm then A

Question

In a right angled $△ A BC .$ $m ∠ A BC = 9 0^{o}$ , $m ∠ = 3 0^{o}$ . If $BC = 9$ cm then $A C$ ?

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Noah Discussed

In a right angled

△ A BC .

m ∠ A BC = 9 0^{o}

m ∠ = 3 0^{o}

. If

BC = 9

cm then

A C

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Given

∠ A BC = 9 0^{o}

∠ A = 3 0^{o}

BC = 9

To find AC

In rt

Δ A BC

tan 3 0^{o} = \frac{BC}{A B}

\frac{1}{3} = \frac{BC}{A B}

\Rightarrow A B = 3 BC

= 3 (9)

= 93

cm.

By Pythagoras theorem,

(A C)^{2} = (A B)^{2} + (BC)^{2}

= (93)^{2} + 9^{2}

= 9^{2} (3) + 9^{2}

= 9^{2} (3 + 1)

= 9^{2} (4) = 324

A C = 324 = 18

cm.

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Question Text	In a right angled $△ A BC .$ $m ∠ A BC = 9 0^{o}$ , $m ∠ = 3 0^{o}$ . If $BC = 9$ cm then $A C$ ?
Answer Type	Text solution:1
Upvotes	150