Worksheet: The Cosine Ratio

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In this worksheet, we will practice finding missing lengths and angles in a triangle using the cosine ratios.

Q1:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐴𝐵=26cm and 𝑚∠𝐴=64∘. Find the length of 𝐴𝐶 giving the answer to two decimal places.

Q2:

Find the length of 𝐴𝐵 giving the answer to two decimal places.

Q3:

𝐴 𝐵 𝐶 𝐷 is a rectangle where the diagonal 𝐴𝐶=4cm and 𝑚∠𝐴𝐶𝐵=27∘. Find the length of 𝐵𝐶 giving the answer to two decimal places.

Q4:

In the given figure, 𝑚∠𝐵𝐴𝐶=90∘ and 𝐴𝐷⟂𝐵𝐶. What is 𝐵𝐶𝜃cos?

  • A 𝐴 𝐷
  • B 𝐴 𝐶
  • C 𝐷 𝐵
  • D 𝐵 𝐶
  • E 𝐴 𝐵

Q5:

A swimming pool is in the shape of a trapezium. Find the length of one of the equal sides giving the answer to one decimal place.

Q6:

Find the radius of circle 𝑀 given 𝐴𝐶=14cm and 𝑚∠𝐴=50∘. Give the answer to two decimal places.

Q7:

𝐴 𝐵 𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=10cm and 𝑚∠𝐶=5220′21′′∘. Find the length of 𝐵𝐶 giving the answer to one decimal place.

Q8:

𝐴 𝐵 𝐶 is a triangle, where 𝐴𝐵=𝐴𝐶, 𝐵𝐶=34cm, and 𝑚∠𝐵=4913′29′′∘. Find the length of 𝐴𝐵, giving your answer to the nearest centimeter.

Q9:

In the given figure, find the length of 𝐴𝐶 to two decimal places.

Q10:

For the figure given, find 𝑥 to two decimal places.

Q11:

Find 𝑥. Give your answer to two decimal places.

Q12:

𝐴 𝐵 𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=5.8cm and 𝑚∠𝐵=488′32′′∘. Find the length of 𝐵𝐶 giving the answer to one decimal place.

Q13:

Find the length of 𝐴𝐵 giving the answer to two decimal places.

Q14:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐴𝐵=15cm and 𝑚∠𝐴=64∘. Find the length of 𝐴𝐶 giving the answer to two decimal places.

Q15:

𝐴 𝐵 𝐶 𝐷 is a rectangle where the diagonal 𝐴𝐶=22cm and 𝑚∠𝐴𝐶𝐵=75∘. Find the length of 𝐵𝐶 giving the answer to two decimal places.

Q16:

A swimming pool is in the shape of a trapezium. Find the length of one of the equal sides giving the answer to one decimal place.

Q17:

Find the radius of circle 𝑀 given 𝐴𝐶=7cm and 𝑚∠𝐴=28∘. Give the answer to two decimal places.

Q18:

𝐴 𝐵 𝐶 𝐷 is an isosceles trapezium where 𝐴𝐵=𝐴𝐷=𝐷𝐶=10cm and 𝐵𝐶=16cm. Find 𝑚∠𝐵 and 𝑚∠𝐴 giving the answer to the nearest second.

  • A 𝑚 ∠ 𝐵 = 7 2 3 2 ′ 3 3 ′ ′ ∘ , 𝑚 ∠ 𝐴 = 1 7 2 7 ′ 2 7 ′ ′ ∘
  • B 𝑚 ∠ 𝐵 = 7 2 3 2 ′ 3 3 ′ ′ ∘ , 𝑚 ∠ 𝐴 = 1 0 7 2 7 ′ 2 7 ′ ′ ∘
  • C 𝑚 ∠ 𝐵 = 1 7 2 7 ′ 2 7 ′ ′ ∘ , 𝑚 ∠ 𝐴 = 7 2 3 2 ′ 3 3 ′ ′ ∘
  • D 𝑚 ∠ 𝐵 = 1 7 2 7 ′ 2 7 ′ ′ ∘ , 𝑚 ∠ 𝐴 = 1 6 2 3 2 ′ 3 3 ′ ′ ∘

Q19:

In the given figure, 𝑚∠𝐵𝐴𝐶=90∘ where 𝐴𝐷⊥𝐵𝐶. What is the value of 𝐴𝐵𝜃cos?

  • A 𝐴 𝐵
  • B 𝐴 𝐶
  • C 𝐴 𝐷
  • D 𝐵 𝐷
  • E 𝐵 𝐶

Q20:

Find the value of cos𝐵.

  • A 1 5 3 1
  • B 3 1 3 4
  • C 1 5 3 4
  • D 1 5 1 7

Q21:

In the given figure, the two triangles are similar.

Work out the value of cos𝜃 for △𝐴𝐵𝐶. Give your answer as a fraction in its simplest form.

  • A 4 5
  • B 3 5
  • C 4 3
  • D 5 4
  • E 3 4

Work out the value of cos𝜃 for △𝐸𝐹𝐷. Give your answer as a fraction in its simplest form.

  • A 3 4
  • B 4 3
  • C 3 5
  • D 5 4
  • E 4 5

What can be said about the value of cos𝜃 for two similar triangles?

  • AThey are often equal.
  • BThey are always equal.
  • CThere is no relation.

Q22:

Find the value of 𝑥𝐵+𝑦𝐴coscos.

Q23:

A 20-feet ladder leans against the side of the building such that the bottom of the ladder is 4 feet from the bottom of the building. Health and safety specifications require the measure of the angle between the ladder and the ground to be between 75∘ and 76∘. Does the ladder satisfy those specifications?

  • Ano
  • Byes

Q24:

𝐴 𝐵 𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=13cm and 𝐵𝐶=24cm. Find the value of cos∠𝐶𝐴𝐷 given 𝐷 lies on 𝐵𝐶 where 𝐴𝐷⟂𝐵𝐶.

  • A 1 3 2 4
  • B 1 3 1 2
  • C 1 2 1 3
  • D 1 3 5
  • E 5 1 3

Q25:

A student rests their 15 cm ruler against a pen pot such that it makes an angle of 42∘ with the horizontal desk. How far is the bottom of the ruler from the bottom of the pot? Give your answer in centimeters to one decimal place.

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