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Lesson: The Cosine Ratio

Video

12:38

Sample Question Videos

Worksheet • 15 Questions • 1 Video

Q1:

𝐴 𝐡 𝐢 𝐷 is an isosceles trapezium where 𝐴 𝐡 = 𝐴 𝐷 = 𝐷 𝐢 = 1 0 c m and 𝐡 𝐢 = 1 6 c m . Find π‘š ∠ 𝐡 and π‘š ∠ 𝐴 giving the answer to the nearest second.

  • A π‘š ∠ 𝐡 = 7 2 3 2 β€² 3 3 β€² β€² ∘ , π‘š ∠ 𝐴 = 1 0 7 2 7 β€² 2 7 β€² β€² ∘
  • B π‘š ∠ 𝐡 = 7 2 3 2 β€² 3 3 β€² β€² ∘ , π‘š ∠ 𝐴 = 1 7 2 7 β€² 2 7 β€² β€² ∘
  • C π‘š ∠ 𝐡 = 1 7 2 7 β€² 2 7 β€² β€² ∘ , π‘š ∠ 𝐴 = 7 2 3 2 β€² 3 3 β€² β€² ∘
  • D π‘š ∠ 𝐡 = 1 7 2 7 β€² 2 7 β€² β€² ∘ , π‘š ∠ 𝐴 = 1 6 2 3 2 β€² 3 3 β€² β€² ∘

Q2:

In the given figure, π‘š ∠ 𝐡 𝐴 𝐢 = 9 0 ∘ where 𝐴 𝐷 βŠ₯ 𝐡 𝐢 . What is the value of 𝐴 𝐡 πœƒ c o s ?

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

Q3:

Find the value of c o s 𝐡 .

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

Q4:

Find the value of c o s 𝐡 .

  • A 1 3
  • B 2 0 2 1
  • C 7 2 0
  • D 2 3

Q5:

𝐴 𝐡 𝐢 𝐷 is a rhombus whose diagonals intersect at the point 𝑀 where 𝐴 𝐡 = 1 1 c m and 𝐴 𝑀 = 1 0 c m . Find the value of ∠ 𝐡 𝐴 𝐷 giving the answer to the nearest second.

  • A 4 9 1 4 β€² 2 4 β€² β€² ∘
  • B 6 5 2 2 β€² 4 8 β€² β€² ∘
  • C 9 0 2 4 β€² 2 3 β€² β€² ∘
  • D 2 4 3 7 β€² 1 2 β€² β€² ∘
  • E 8 4 3 2 β€² 5 1 β€² β€² ∘

Q6:

𝐴 𝐡 𝐢 𝐷 is a rhombus whose diagonals intersect at the point 𝑀 where 𝐴 𝐡 = 1 6 c m and 𝐴 𝑀 = 1 2 c m . Find the value of ∠ 𝐡 𝐴 𝐷 giving the answer to the nearest second.

  • A 8 2 4 9 β€² 9 β€² β€² ∘
  • B 4 8 3 5 β€² 2 5 β€² β€² ∘
  • C 7 8 6 β€² 3 6 β€² β€² ∘
  • D 4 1 2 4 β€² 3 5 β€² β€² ∘
  • E 7 3 4 4 β€² 2 3 β€² β€² ∘

Q7:

𝐴 𝐡 𝐢 𝐷 is a rhombus whose diagonals intersect at the point 𝑀 where 𝐴 𝐡 = 1 8 c m and 𝐴 𝑀 = 7 c m . Find the value of ∠ 𝐡 𝐴 𝐷 giving the answer to the nearest second.

  • A 1 3 4 1 3 β€² 4 5 β€² β€² ∘
  • B 2 2 5 3 β€² 7 β€² β€² ∘
  • C 4 3 2 6 β€² 5 5 β€² β€² ∘
  • D 6 7 6 β€² 5 3 β€² β€² ∘
  • E 4 2 3 0 β€² 4 β€² β€² ∘

Q8:

In the given figure, the two triangles are similar.

Work out the value of c o s πœƒ for β–³ 𝐴 𝐡 𝐢 . Give your answer as a fraction in its simplest form.

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

Work out the value of c o s πœƒ for β–³ 𝐸 𝐹 𝐷 . Give your answer as a fraction in its simplest form.

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

What can be said about the value of c o s πœƒ for two similar triangles?

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

Q9:

Find the value of π‘₯ 𝐡 + 𝑦 𝐴 c o s c o s .

Q10:

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 7 5 ∘ and 7 6 ∘ . Does the ladder satisfy those specifications?

  • Ayes
  • Bno

Q11:

𝐴 𝐡 𝐢 is an isosceles triangle where 𝐴 𝐡 = 𝐴 𝐢 = 1 3 c m and 𝐡 𝐢 = 2 4 c m . Find the value of c o s 𝐢 𝐴 𝐷 given 𝐷 lies on 𝐡 𝐢 where  𝐴 𝐷 βŸ‚ 𝐡 𝐢 .

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

Q12:

A student rests their 15 cm ruler against a pen pot such that it makes an angle of 4 2 ∘ 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.

Q13:

A ladder is leaning against a vertical wall where the angle of inclination with the ground is π‘š ∠ 𝛼 = 4 7 ∘ . The lower end of the ladder moves 𝑠 = 6 metres away from the wall and the angle of inclination becomes π‘š ∠ πœƒ = 3 0 ∘ . Find the length of the ladder giving the answer to one decimal place.

Q14:

A 13-foot ladder leans against a window sill which is 12 feet above ground level. Find, in radians to the nearest three decimal places, the angle the ladder makes with the wall of the building.

Q15:

A 23-foot ladder leans against the wall of a house. If the bottom of the ladder is more than 7 feet from the bottom of the wall, it will slip. What is the angle the ladder makes with the ground when it starts to slip? Give your answer to two decimal places.

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