Question

What is the length of LJ?

Answer 1

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.

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

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.

$\frac{l}{\sin L}=\frac{j}{\sin J}=\frac{k}{\sin K}$

Take only two sides.

$\frac{9}{\sin 89^\circ}=\frac{LJ}{\sin 23^\circ}$

$9\times \sin 23^\circ=LJ \times\sin 89^\circ$

$9\times0.3907=LJ \times0.9998$

$3.5163=LJ \times0.9998$

$LJ=\frac{3.5163}{0.9998}$

$LJ=3.51$

LJ = 3.5 (approximately)

Option D is the correct answer.

The length of LJ = 3.5.