Worksheet: The Cosine Ratio

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

Q1:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐴 𝐵 = 2 6 c m and 𝑚 ∠ 𝐴 = 6 4 ∘ . Find the length of 𝐴 𝐶 giving the answer to two decimal places.

Q2:

Find the length of 𝐴 𝐵 giving the answer to two decimal places.

Q3:

𝐴 𝐵 𝐶 𝐷 is a rectangle where the diagonal 𝐴 𝐶 = 4 c m and 𝑚 ∠ 𝐴 𝐶 𝐵 = 2 7 ∘ . Find the length of 𝐵 𝐶 giving the answer to two decimal places.

Q4:

In the given figure, 𝑚 ∠ 𝐵 𝐴 𝐶 = 9 0 ∘ and 𝐴 𝐷 ⟂ 𝐵 𝐶 . What is 𝐵 𝐶 𝜃 c o s ?

  • A 𝐴 𝐷
  • B 𝐴 𝐵
  • C 𝐵 𝐶
  • D 𝐴 𝐶
  • E 𝐷 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 𝐴 𝐶 = 1 4 c m and 𝑚 ∠ 𝐴 = 5 0 ∘ . Give the answer to two decimal places.

Q7:

𝐴 𝐵 𝐶 is an isosceles triangle where 𝐴 𝐵 = 𝐴 𝐶 = 1 0 c m and 𝑚 ∠ 𝐶 = 5 2 2 0 ′ 2 1 ′ ′ ∘ . Find the length of 𝐵 𝐶 giving the answer to one decimal place.

Q8:

𝐴 𝐵 𝐶 is a triangle, where 𝐴 𝐵 = 𝐴 𝐶 , 𝐵 𝐶 = 3 4 c m , and 𝑚 ∠ 𝐵 = 4 9 1 3 ′ 2 9 ′ ′ ∘ . Find the length of 𝐴 𝐵 , giving your answer to the nearest centimetre.

Q9:

In the given figure, find the length of 𝐴 𝐶 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 𝐴 𝐵 = 𝐴 𝐶 = 5 . 8 c m and 𝑚 ∠ 𝐵 = 4 8 8 ′ 3 2 ′ ′ ∘ . Find the length of 𝐵 𝐶 giving the answer to one decimal place.

Q13:

Find the length of 𝐴 𝐵 giving the answer to two decimal places.

Q14:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐴 𝐵 = 1 5 c m and 𝑚 ∠ 𝐴 = 6 4 ∘ . Find the length of 𝐴 𝐶 giving the answer to two decimal places.

Q15:

𝐴 𝐵 𝐶 𝐷 is a rectangle where the diagonal 𝐴 𝐶 = 2 2 c m and 𝑚 ∠ 𝐴 𝐶 𝐵 = 7 5 ∘ . Find the length of 𝐵 𝐶 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 𝐴 𝐶 = 7 c m and 𝑚 ∠ 𝐴 = 2 8 ∘ . Give the answer to two decimal places.

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