Question

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

Answer 1

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.