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If the area of the triangle ABC is 450 cm2. measure of angle B = 82° , C = 56° , find the value of a.​

1 Answer

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Answer:

If the area of the triangle ABC is
450 \mathrm{cm}^(2) ,then value of a is 27cm.

Solution:

Given Data:

Area of the triangle ABC is
450 \mathrm{cm}^(2)


\angle \mathrm{B}=82^(\circ)


\angle \mathrm{C}=56^(0)

To Find:

Value of a?

Step 1:


\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^(\circ)


\angle \mathrm{A}=42^(0)

Step 2:


\mathrm{E}=(1)/(2) \alpha \mathrm{b} \sin \mathrm{C}

By Law of Sines


(\alpha)/(\sin A)=(b)/(\sin B)

Simplify the above expression


\mathrm{b}=(\alpha \sin B)/(\sin A)


E=(1)/(2) \alpha\left((\alpha \sin B)/(\sin A)\right) \sin C --- eqn 1

Step 3:


\begin{aligned} E &=(1)/(2) \alpha^(2)\left((\sin B \sin C)/(\sin A)\right) \\ \alpha &=\sqrt{(2 E \sin A)/(\sin B \sin C)} \end{aligned}

Step 4:

Substitute the A, B and C value from the given Data.


\alpha=\sqrt{(2.450 \sin 42^(\circ))/(\sin 82^(\circ) \sin 56^(\circ))}

Apply the Sin theta respective value.


=\sqrt{(602.22)/(0,82)}


\alpha=>27 \mathrm{cm}

From the above we finally got the value of "a" which is 27 cm.

User Serhii Soboliev
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