Question

In ΔHIJ, h = 40 cm, ∠J=20° and ∠H=93°. Find the length of j, to the nearest centimeter.

Answer 1

Given:

In ΔHIJ, h = 40 cm, ∠J=20° and ∠H=93°.

To find:

The length of j, to the nearest centimeter.

Solution:

According to Law of sine,

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

In ΔHIJ, using law of sine, we get

$\dfrac{j}{\sin J}=\dfrac{h}{\sin H}$

$\dfrac{j}{\sin (20^\circ)}=\dfrac{40}{\sin (93^\circ)}}$

$j=\dfrac{40\times \sin (20^\circ)}{\sin (93^\circ)}}$

On further simplification, we get

$j=\dfrac{40\times 0.34202}{0.99863}$

$j=\dfrac{13.6808}{0.99863}$

$j=13.69958$

Approximate the value to the nearest centimeter.

$j\approx 14$

Therefore, the length of j is 14 cm.