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Cecil P1

The document contains a series of mathematical problems involving right-angled triangles, trigonometric functions, and geometric calculations. It includes tasks such as calculating the height of a building using distances, finding the lengths of triangle sides, and evaluating trigonometric ratios. Additionally, it presents problems related to kite flying and the use of sine, cosine, and tangent values.

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vanessa.livania2
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11 views2 pages

Cecil P1

The document contains a series of mathematical problems involving right-angled triangles, trigonometric functions, and geometric calculations. It includes tasks such as calculating the height of a building using distances, finding the lengths of triangle sides, and evaluating trigonometric ratios. Additionally, it presents problems related to kite flying and the use of sine, cosine, and tangent values.

Uploaded by

vanessa.livania2
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1. The distance from a point on the ground to the base of the building is 15 metres.

The distance
from a point on the ground to the top of the building is 25 metres. Calculate the height of the
building.

25 m
𝑥

15 m

2. Work out the length of DA and leave your answer in the exact form.

8 cm

7 cm

5 cm
3. ABC is a right-angled triangle.

ABC is a right-angled triangle. If AB = 8 cm and AC = 10 cm.


a) Find the exact value of BC.
b) Find sin 𝐴𝐶𝐵
c) Find cos 𝐴𝐶𝐵
d) Find tan 𝐴𝐶𝐵
e) Find sin 𝐶𝐴𝐵
f) Find cos 𝐶𝐴𝐵
g) Find tan 𝐶𝐴𝐵
1 √3 √3
4. Given sin 30 = , cos 30 = , tan 30 =
2 2 3

Find the value of 𝑥.

√3 √2 √3
5. Given sin 60 = , cos 45 = , tan 30 = . Calculate:
2 2 2
a) (sin 60)2 + cos 45 =
b) (sin 60)2 + (tan 30)2 =
c) sin 60 − (cos 45)2 =
d) (sin 60 − cos 45) ÷ tan 30 =
e) (sin 60 − cos 45) × tan 30 =
f) (sin 60)2 + (cos 45)2 + (tan 30)2 =

6. A person flying a kite has released 750 m of string. The string makes an angle of 60° with the
√3 1
ground. If sin 60 = , cos 60 = 𝑎𝑛𝑑 tan 60 = √3, find the height of the kite from the
2 2
ground.

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