Download Worksheet: Trigonometry Test (QQQ)

QQQ – Trigonometry
Name __________________
5 An angle in a right-angled triangle is 75°.
What is the ratio of the lengths of the
opposite side to the hypotenuse?
______________
1 Determine x.
6 In a right-angled triangle, the opposite
side to an angle 𝜃 has length 4 and the
hypotenuse has length 5. What is
cos⁡(𝜃)?
3
x
35°
______________
x = _________ (to 2dp)
2 Determine y.
7 Determine x (Hint: find the length of the
right-most line first)
3
38°
y
35°
y = _________ (to 2dp)
65°
x
3 Determine θ.
3
θ
4
θ = ______° (to 2dp)
4 A cat is stuck at the top of a tree which is
20m high. You have a ladder which is
30m long, and you place the ladder such
that the top is right by the cat. What is
the angle of inclination of the ladder to
the ground?
7
x = ____________ (to 2dp)
8 A cube sits on a table. What is the angle
of inclination of the line between a
bottom corner and the opposite top
corner, relative to the surface of the
table?
θ
θ=⁡_____________
______° (to 2dp)
Score ________ / 8
Award ___________
QQQ – Trigonometry - ANSWERS
1 Determine x.
5 An angle in a right-angled triangle is 75°.
What is the ratio of the lengths of the
opposite side to the hypotenuse?
0.97 : 1 (the :1 is optional)
3
x
6 In a right-angled triangle, the opposite
side to an angle 𝜃 has length 4 and the
hypotenuse has length 5. What is
cos⁡(𝜃)?
𝟑
𝟓
35°
x = 1.72
2 Determine y.
7 Determine x (Hint: find the length of the
right-most line first)
3
38°
y
y = 3.84
35°
x
3 Determine θ.
3
θ
4
θ = 36.87°
4 A cat is stuck at the top of a tree which is
20m high. You have a ladder which is
30m long, and you place the ladder such
that the top is right by the cat. What is
the angle of inclination of the ladder to
the ground?
41.81°
65°
7
x = 14.44
8 A cube sits on a table. What is the angle
of inclination of the line between a
bottom corner and the opposite top
corner, relative to the surface of the
table?
θ
θ=⁡35.26°