Worksheet: Trigonometric Ratios in Right Triangles

In this worksheet, we will practice finding the angles of a right triangle and their trigonometric functions using the ratios between the triangle’s side lengths.

Q1:

What is the value of c o s πœƒ in the given triangle?

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

Q2:

Find c o s 𝐴 , given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐢 where 𝐴 𝐡 = 1 0 c m and 𝐡 𝐢 = 6 c m .

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

Q3:

What is the value of c o s πœƒ in the given triangle?

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

Q4:

Find s i n 𝐡 , given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐢 where 𝐴 𝐡 = 1 7 c m and 𝐡 𝐢 = 1 5 c m .

  • A 1 5 1 7
  • B 1 7 8
  • C 1 7 1 5
  • D 8 1 7

Q5:

What is the value of s i n πœƒ in the given triangle?

  • A √ 2
  • B1
  • C 1 + √ 2
  • D √ 2 2
  • E2

Q6:

What is the value of s i n πœƒ in the given triangle?

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

Q7:

Find c o s 𝐡 , given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐢 where 𝐴 𝐡 = 1 7 c m and 𝐡 𝐢 = 1 5 c m .

  • A 8 1 7
  • B 1 7 1 5
  • C 1 7 8
  • D 1 5 1 7

Q8:

What is the value of t a n πœƒ in the given triangle?

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

Q9:

𝐴 𝐡 𝐢 is an isosceles triangle where 𝐴 𝐡 = 𝐴 𝐢 = 1 0 c m and 𝐡 𝐢 = 1 6 c m . Find the value of s i n 𝐢 𝐴 𝐷 given that 𝐷 is the midpoint of 𝐡 𝐢 .

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

Q10:

𝐴 𝐡 𝐢 is a triangle, where the ratio between its lengths π‘Ž , 𝑏 , and 𝑐 is 4 ∢ 3 ∢ 5 . Find s i n 𝐴 .

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

Q11:

Find the value of 2 𝐴 βˆ’ 1 s i n 2 given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 where 𝐡 𝐢 = 1 0 c m and 𝐴 𝐢 = 2 6 c m .

  • A βˆ’ 1 6 9 1 1 9
  • B 1 1 9 1 6 9
  • C βˆ’ 4 7 7 2
  • D βˆ’ 1 1 9 1 6 9

Q12:

Find the value of t a n s i n c o s 𝐢 𝐢 𝐢 given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐴 where t a n 𝐡 = 1 .

  • A √ 2 2
  • B 1 4
  • C2
  • D 1 2

Q13:

Find c o s 𝐡 , given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐢 where 𝐴 𝐡 = 1 5 c m and 𝐡 𝐢 = 1 2 c m .

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

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