Worksheet: The Cosine Ratio

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

Q1:

𝐴𝐵𝐶 is a right 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:

𝐴𝐵𝐶𝐷 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?

  • A𝐴𝐷
  • B𝐴𝐶
  • C𝐷𝐵
  • D𝐵𝐶
  • E𝐴𝐵

Q5:

A swimming pool is in the shape of a trapezoid. 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:

𝐴𝐵𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=10cm and 𝑚𝐶=522021. Find the length of 𝐵𝐶 giving the answer to one decimal place.

Q8:

𝐴𝐵𝐶 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:

𝐴𝐵𝐶 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:

𝐴𝐵𝐶 is a right triangle at 𝐵 where 𝐴𝐵=15cm and 𝑚𝐴=64. Find the length of 𝐴𝐶 giving the answer to two decimal places.

Q15:

𝐴𝐵𝐶𝐷 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 trapezoid. 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:

𝐴𝐵𝐶𝐷 is an isosceles trapezoid where 𝐴𝐵=𝐴𝐷=𝐷𝐶=10cm and 𝐵𝐶=16cm. Find 𝑚𝐵 and 𝑚𝐴 giving the answer to the nearest second.

  • A𝑚𝐵=723233, 𝑚𝐴=172727
  • B𝑚𝐵=723233, 𝑚𝐴=1072727
  • C𝑚𝐵=172727, 𝑚𝐴=723233
  • D𝑚𝐵=172727, 𝑚𝐴=1623233

Q19:

In the given figure, 𝑚𝐵𝐴𝐶=90 where 𝐴𝐷𝐵𝐶. What is the value of 𝐴𝐵𝜃cos?

  • A𝐴𝐵
  • B𝐴𝐶
  • C𝐴𝐷
  • D𝐵𝐷
  • E𝐵𝐶

Q20:

Find the value of cos𝐵.

  • A1531
  • B3134
  • C1534
  • D1517

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.

  • A45
  • B35
  • C43
  • D54
  • E34

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

  • A34
  • B43
  • C35
  • D54
  • E45

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:

𝐴𝐵𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=13cm and 𝐵𝐶=24cm. Find the value of cos𝐶𝐴𝐷 given 𝐷 lies on 𝐵𝐶 where 𝐴𝐷𝐵𝐶.

  • A1324
  • B1312
  • C1213
  • D135
  • E513

Q24:

A ladder is leaning against a vertical wall where the angle of inclination with the ground is 𝑚𝛼=47. The lower end of the ladder moves 𝑠=6 metres away from the wall and the angle of inclination becomes 𝑚𝜃=30. Find the length of the ladder giving the answer to one decimal place.

Q25:

Find 𝑚𝐵 given 𝐴𝐵𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=25cm and 𝐵𝐶=40cm. Give the answer to the nearest second.

  • A365212
  • B383935
  • C53748
  • D512025

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