Question

In triangle ABC ,right angle is at B,Ab=5cm and angle ACB =30.Determine the length of the sides BC and Ac

Answer 1

Hello Friend....

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The answer of u r question is.....

Ans:

Given,

AB=5cm

Angle ACB=30°....

To find the length of side BC,we will choose the trigonometric ratio involving BC and the given side AB.

since,

BC is the side adjacent to angle C and AB is the side opposite to angle C.

Therefore,

AB/BC= tan c

= 5/BC = tan30°

=1/√3

Which gives BC=5/√3 cm..

Now,

by using the Pythagoras theorem

${ac}^{2} = {ab}^{2} + {bc}^{2}$
${ac}^{2} = {5}^{2} + (5 \sqrt{3) {}^{2} }$
${ac}^{2} = 25 + 75$

Ac=√100

=10 cm...

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Answer 2

HEYA!!!


HERE IS YOUR ANSWER,


=> (Hypotnuese)² = sum of the squares of the two sides,

Whereas,

=> Hypotnuese is the side which is opposite to 90°.

=> Now, since this problem has following given in itself:

=> Side AB = 5 cm

=> Angle B = 90°.

=> Angle ACB = 30 Deg.

=> So we can use the following formula of trigonometry,

=> Tangent of angle = (Opposite side) / (Adjacent side)

=> Therefore, tan 30 = 5 / BC,

However,

=> tan30 = 1/√3.

So it means,

=> 1/√3 = 5/(side BC),

Therefore,

=> Required side BC = 5√3 cm.

Now,

=> sin 30 = (side opp. to angle C) / (hypotenuse)

=> 1/2 = AB/AC

=> 1/2 = 5/AC

=> AC = 10 cm.

Therefore,

=> Required side AC = 10 cm.


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