Option D:
The length of LJ = 3.5
Solution:
In the triangle LJK,
LK = 9, ∠K = 23°, ∠J = 89°
To find the length of LJ:
Law of sine:
A, B, C are the angles of the triangle and
a, b, c are the sides of the triangle.
[tex]$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
Here for ΔLJK,
The side opposite to angle L is l.
The side opposite to angle J is j.
The side opposite to angle K is k.
[tex]$\frac{l}{\sin L}=\frac{j}{\sin J}=\frac{k}{\sin K}[/tex]
Take only two sides.
[tex]$\frac{9}{\sin 89^\circ}=\frac{LJ}{\sin 23^\circ}[/tex]
[tex]$9\times \sin 23^\circ=LJ \times\sin 89^\circ[/tex]
[tex]$9\times0.3907=LJ \times0.9998[/tex]
[tex]$3.5163=LJ \times0.9998[/tex]
[tex]$LJ=\frac{3.5163}{0.9998}[/tex]
[tex]$LJ=3.51[/tex]
LJ = 3.5 (approximately)
Option D is the correct answer.
The length of LJ = 3.5.
