Worksheet: The Cosine Ratio

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 𝑚𝐴=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 𝑚𝐴𝐶𝐵=27. Find the length of 𝐵𝐶 giving the answer to two decimal places.

Q4:

In the given figure, 𝑚𝐵𝐴𝐶=90 and 𝐴𝐷𝐵𝐶. 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 𝑚𝐴=50. Give the answer to two decimal places.

Q7:

𝐴 𝐵 𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=10cm and 𝑚𝐶=522021. 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 𝑚𝐵=491329. 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 𝑚𝐵=48832. 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 𝑚𝐴=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 𝑚𝐴𝐶𝐵=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 𝑚𝐴=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 𝑚𝐵 and 𝑚𝐴 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, 𝑚𝐵𝐴𝐶=90 where 𝐴𝐷𝐵𝐶. 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 cos𝐶𝐴𝐷 given 𝐷 lies on 𝐵𝐶 where 𝐴𝐷𝐵𝐶.

  • 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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