What is the length of LJ?

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.

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.

Take only two sides.

LJ = 3.5 (approximately)

Option D is the correct answer.

The length of LJ = 3.5.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west