Mathematics: Application and Interpretations 11
Sekolah Cikal Lebak Bulus
Name :
Class :
Triangle Trigonometry
1. [Maximum mark: 6]
The diagram below shows a triangle ABC. The size of angle ∠𝐴𝑀𝐶 is 150°, where 𝑀
is the midpoint of 𝐴𝐵. 𝑀𝐵𝐶 is an isosceles triangle, with 𝑀𝐶 = 𝑀𝐵 = 4𝑐𝑚.
a.
b.
c.
d.
Write down the length of 𝐴𝑀.
Find the size of angle ∠𝐶𝑀𝐵.
Find the size of angle ∠𝐴𝐵𝐶.
Find the length of 𝐶𝐵.
[1]
[1]
[2]
[2]
2. [Maximum mark: 6]
A national park is in the form of a triangle,𝐴𝐵𝐶, as shown in the following diagram.
Side length 𝐴𝐵 is 49 𝑘𝑚 and side length 𝐵𝐶 is 66 𝑘𝑚. Angle ∠𝐴𝐵𝐶 is 58°.
a. Calculate the side length 𝐴𝐶 in 𝑘𝑚.
b. Calculate the area of the park.
[3]
[3]
3. [Maximum mark: 6]
The diagram below shows quadrilateral ABCD with side lengths of 𝐴𝐷 = 12 𝑚, 𝐷𝐶 =
7 𝑚, and 𝐵𝐶 = 5𝑚. Angle ∠𝐵𝐴𝐷 = 50° and angle ∠𝐵𝐶𝐷 = 100°.
A new line is drawn from 𝐵 to 𝐷 direct.
a. Calculate the length of this new line, 𝐵𝐷.
b. Calculate the size of angle ∠𝐴𝐵𝐷.
[3]
[3]
4. [Maximum mark: 10]
The sides of a triangle 𝐴𝐵𝐶 have the following lengths 𝐴𝐵 = 40𝑚𝑚, 𝐵𝐶 = 30𝑚𝑚, and
𝐶𝐴 = 55𝑚𝑚.
a. Calculate the size of the angle ∠𝐴𝐵𝐶.
b. Calculate the area of the triangle 𝐴𝐵𝐶.
[3]
[2]
A point 𝐷 is located outside of the triangle, such that angle ∠𝐷𝐴𝐵 = 80° and angle
∠𝐷𝐵𝐴 = 10°.
c. Show that the angle ∠𝐴𝐷𝐵 is 90°.
[1]
d. Find the distances 𝐴𝐷 and 𝐵𝐷.
[4]