MATH 321 INFORMAL ASSESSMENT STUDY UNIT 5
1.
In the diagram below, BC is a pole anchored by two cables at A and D. A, D and C
are in the same horizontal plane. The height of the pole is ℎ and the angle of
elevation from A to the top of the pole, B is 𝛽𝛽. 𝐴𝐴𝐵𝐵�𝐷𝐷 = 2𝛽𝛽 and BA = BD.
Determine the distance AD between the two anchors in terms of h
2. In the figure, K, A and F are in the same horizontal plane and TA represents a
vertical tower.
𝐴𝐴𝑇𝑇�𝐾𝐾 = 𝑥𝑥, 𝐾𝐾𝐴𝐴̂𝐹𝐹 = 90° + 𝑥𝑥 and 𝐾𝐾𝐹𝐹� 𝐴𝐴 = 2𝑥𝑥 where 0° < 𝑥𝑥 < 30°. TK = 2 units
2.1
Express AK in terms of sin𝑥𝑥
2.2
Calculate the numerical value of KF
3.
In the diagram below , B, C and D are in the same horizontal plane. A drone positioned at A
captures the images of two objects at B and C. B is directly below the drone and c is 4 units
away from B.
𝐷𝐷𝐶𝐶̂ 𝐵𝐵 = 60°; 𝐷𝐷𝐵𝐵�𝐶𝐶 = 120° − 𝛼𝛼 and 𝐷𝐷𝐴𝐴̂𝐵𝐵 = 90° − 𝜃𝜃
3.1
3.2
3.3
�1 in terms of 𝛼𝛼
Determine 𝐷𝐷
Without the use of a calculator, determine BD in terms of 𝛼𝛼
Prove that 𝐴𝐴𝐴𝐴 =
2√3𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠