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Worksheet: The Cosine Ratio

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

Q1:

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

Q2:

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

Q3:

is a right triangle at where and . Find the length of giving the answer to two decimal places.

  • A 12.68 cm
  • B 59.31 cm
  • C 11.40 cm
  • D 28.93 cm
  • E 53.31 cm

Q4:

is a right triangle at where and . Find the length of giving the answer to two decimal places.

  • A 7.32 cm
  • B 34.22 cm
  • C 6.58 cm
  • D 16.69 cm
  • E 30.75 cm

Q5:

𝐴 𝐡 𝐢 𝐷 is a rectangle where the diagonal 𝐴 𝐢 = 4 c m and π‘š ∠ 𝐴 𝐢 𝐡 = 2 7 ∘ . Find the length of 𝐡 𝐢 giving the answer to two decimal places.

Q6:

𝐴 𝐡 𝐢 𝐷 is a rectangle where the diagonal 𝐴 𝐢 = 2 2 c m and π‘š ∠ 𝐴 𝐢 𝐡 = 7 5 ∘ . Find the length of 𝐡 𝐢 giving the answer to two decimal places.

Q7:

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.

  • A 10.8 m
  • B 9.5 m
  • C 15.3 m
  • D 8.8 m
  • E 13.4 m

Q8:

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.

  • A 7.2 m
  • B 5 m
  • C 10.4 m
  • D 8.8 m
  • E 9.2 m

Q9:

𝐴 𝐡 𝐢 is a triangle, where 𝐴 𝐡 = 𝐴 𝐢 , 𝐡 𝐢 = 3 4 c m , and π‘š ∠ 𝐡 = 4 9 1 3 β€² 2 9 β€² β€² ∘ . Find the length of 𝐴 𝐡 , giving your answer to the nearest centimeter.

  • A 11 cm
  • B 22 cm
  • C 13 cm
  • D 26 cm

Q10:

In the given figure, π‘š ∠ 𝐡 𝐴 𝐢 = 9 0 ∘ and 𝐴 𝐷 βŸ‚ 𝐡 𝐢 . What is 𝐡 𝐢 πœƒ c o s ?

  • A 𝐴 𝐷
  • B 𝐴 𝐡
  • C 𝐡 𝐢
  • D 𝐴 𝐢
  • E 𝐷 𝐡

Q11:

Find the radius of circle 𝑀 given 𝐴 𝐢 = 1 4 c m and π‘š ∠ 𝐴 = 5 0 ∘ . Give the answer to two decimal places.

Q12:

Find the radius of circle 𝑀 given 𝐴 𝐢 = 7 c m and π‘š ∠ 𝐴 = 2 8 ∘ . Give the answer to two decimal places.

Q13:

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

Q14:

𝐴 𝐡 𝐢 is an isosceles triangle where 𝐴 𝐡 = 𝐴 𝐢 = 1 0 c m and π‘š ∠ 𝐢 = 5 2 2 0 β€² 2 1 β€² β€² ∘ . Find the length of 𝐡 𝐢 giving the answer to one decimal place.

Q15:

For the figure given, find π‘₯ to two decimal places.

Q16:

Find π‘₯ . Give your answer to two decimal places.

Q17:

is an isosceles triangle where and . Find the length of giving the answer to one decimal place.

  • A 4.3 cm
  • B 6.5 cm
  • C 3.9 cm
  • D 7.7 cm

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