Question

Valerie lives 2 miles west of her school and her friend Yuri lives 3 miles directly northeast of her.

a. Draw a diagram representing this situation.
b. How far does Yuri live from school?
c. What is the bearing of the school to Yuri’s house?

Answer 1

Explanation:

a) The diagram representing this situation is shown in the attached photo.

V represents the position of Valerie.

S represents the position of the school.

Y represents the position of Yuri.

b) v represents the distance of Yuri from the school. To determine v, we would apply the cosine rule,

a^2 = b^2 + c^2 - 2bcCosA

Therefore,

v^2 = 3^2 + 2^2 - 2 × 3 × 2Cos45

v^2 = 11 - 12 × 0.7071

v^2 = 11 - 8.42 = 2.58

v = √2.58

v = 1.61

c) to fine angle Y, we would apply

the sine rule. It is expressed as

a/sinA = b/sinB = c/sin C

2/SinY = 1.61/Sin45

2Sin45 = 1.61SinY

2 × 0.7071 = 1.61SinY

SinY = 1.4034/1.61 = 0.8717

Y = 60.66 degrees

The bearing of the school from Yuri's house would be

180 - 15.66 = 164.34 degrees