Question

In ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°. Find the length of k, to the nearest inch.\

Answer 1

Given:

In  ΔKLM, l = 48 inches, ∠K=55° and ∠L=46°.

To find:

The length of k, to the nearest inch.

Solution:

According to Law of sine,

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

In ΔKLM, using law of sine, we get

$\dfrac{k}{\sin K}=\dfrac{l}{\sin L}$

$\dfrac{k}{\sin (55^\circ)}=\dfrac{48}{\sin (46^\circ)}$

$k=\dfrac{48\times \sin (55^\circ)}{\sin (46^\circ)}$

On further simplification, we get

$k=\dfrac{48\times 0.819152}{0.7193398}$

$k=\dfrac{39.319296}{0.7193398}$

$k=54.66025$

Approximate the value to the nearest inch.

$k\approx 55$

Therefore, the length of k is 55 inch.