MSE2183 Assignment 4 2022

MSE2183 ASSIGNMENT 4 2022

SECTION A

Question 1

1

Activity 6.2




The above polygons are similar.

The corresponding angles have equal measures.
The corresponding sides are in proportion.
The sides on the bigger polygon are twice the size of the corresponding sides on the smaller polygon.

2

Activity 6.5




The coordinates of the vertices of polygon 𝐴𝐵𝐶𝐷𝐸 are multiplied by 2 to get polygon 𝐴′ 𝐵′ 𝐶 ′ 𝐷′ 𝐸 ′

1. The polygons are similar. The shape did not change. The corresponding angles have equal
measures.

2. The dilation took place with respect to the origin (0, 0).

,3

Activity 7.1

Let the height of the pyramid, 𝐸𝐷 = ℎ m




Consider triangle 𝐺𝐻𝐹 where 𝐺𝐻 is perpendicular to 𝐵𝐶




𝑜𝑝𝑝
tan 𝛼 =
𝑎𝑑𝑗

𝐹𝐻
tan 𝛼 =
𝐺𝐻

3
tan 𝛼 =
5

3
𝛼 = tan−1 ( )
5

𝛼 = 30.96°

Therefore, 𝑚∠𝐹𝐺𝐻 = 30.96°

𝑚∠𝐴 = 𝑚∠𝐹𝐺𝐻 (Corresponding angles are equal, 𝐴𝐶 | | 𝐺𝐻)

Therefore, 𝑚∠𝐴 = 30.96°

𝑜𝑝𝑝
tan 𝐴 =
𝑎𝑑𝑗

𝐺𝐵
tan 𝐴 =
𝐴𝐵

2
tan 30.96° =
𝐴𝐵

, 2
𝐴𝐵 =
𝑡𝑎𝑛 30.96°


𝐴𝐵 = 3.33 m




𝐴𝐷 = 3.33 𝑚 + 5 𝑚 + 45 𝑚

𝐴𝐷 = 53.33 𝑚

𝑜𝑝𝑝
tan 𝐴 =
𝑎𝑑𝑗

𝐸𝐷
tan 𝐴 =
𝐴𝐷

ℎ
tan 30.96° =
53.33

ℎ = 53.33 𝑡𝑎𝑛 30.96°

ℎ = 31.99

4

Activity 7.3

𝑜𝑝𝑝
tan 𝜃 =
𝑎𝑑𝑗

ℎ
tan 30° =
25

ℎ = 25 × tan 30°

ℎ = 14.43