Task 1: Murder Mystery

(Click for enlargement)

1. Using trigonometrical concepts, calculate the distance AH.

Solution:

angle C:

tanθ = 139/400

θ = tan^-1 (139)/(400)

θ= 19.16233935

≈ 19.2°

tanθ = O/2480

O = 2480tan19.2°

O = 863.6273732

AH = 863.6273732 + 170 + 370

∴ AH = 1403.627373

≈ 1400 cm

2. Hence, deduce from which storey of the murderer's block the shot was fired. Explain your answer clearly.

Solution:

1400 - 1040 (fourth storey) = 360

180 + 130 = 310 (one storey)

360 - 310 = 50

Answer: 5th storey.

3. What is the bearing of A from B?

Solution:
90 - 19.2 = 70.8°

4. What is the angle of elevation of A from B?

Solution:
tanθ = 139/400
θ = tan^-1 (139)/(400)
θ= 19.16233935
≈ 19.2°

5. State an alternative method that can be used to solve the problem, without the need to use trigonometry.

Solution:
Similar triangles
Two triangles are similar if
- each pair of corresponding angles are equal, and
- each pair of corresponding sides are proportional.