Question

One face of a gemstone is shown below. The longest side is 4.2mm. What are the measures of sides a and b? Jusify you answers.

Answer 1

We can use the trigonometric ratio to obtain the sides a and b

$\begin{gathered} \sin \text{ 35 =}\frac{a}{4.2} \\ \\ 0.5736\text{ =}\frac{a}{4.2} \end{gathered}$

a will be obtained by cross multiplying

a = 4.2 x 0.5736

a = 2.41 mm

To get b

$\sin \text{ 55 =}\frac{b}{4.2}$$0.819\text{ =}\frac{b}{4.2}$

b will be obtained using cross multiplying

b = 0.819 x 4.2

b = 3.44 mm