Question

Determine the approximate value of x.

2.045

3.264

6.736

Answer 1

x = 6.736

Solution:

The image attached below.

Given ∠A = 80°, ∠C = 40° and side a = 5.

Let us first find the measure of ∠B.

Sum of the angles of a triangle = 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ 80° + ∠B + 40° = 180°

⇒ ∠B + 120° = 180°

⇒ ∠B = 180° – 120°

⇒ ∠B = 60°

Let us find the side c using sine law,

$\frac{b}{\sin B}=\frac{c}{\sin C}$

⇒ $\frac{x}{\sin 60^{\circ}}=\frac{5}{\sin 40^{\circ}}$

⇒ $x=\frac{5\times \sin 60^{\circ}}{\sin 40^{\circ}}$

⇒ $x=\frac{5 \times \frac{\sqrt{3}}{2}}{0.6428}$

⇒ $x=\frac{5 \times \sqrt{3}}{2\times {0.6428}}}$

⇒ x = 6.736

Hence, the value of x is 6.736.