Worksheet: Trigonometric Ratios in Right Triangles

In this worksheet, we will practice finding and express the values of the three trigonometric ratios—sine, cosine, and tangent—for a given angle in a right triangle.

Q1:

Find the main trigonometric ratios of 𝐵 given 𝐴𝐵𝐶 is a right-angled triangle at 𝐶 where 𝐴𝐵=30cm and 𝐵𝐶=18cm.

  • Asin𝐵=35, cos𝐵=45, tan𝐵=43
  • Bsin𝐵=45, cos𝐵=35, tan𝐵=43
  • Csin𝐵=35, cos𝐵=45, tan𝐵=34
  • Dsin𝐵=45, cos𝐵=35, tan𝐵=34

Q2:

𝐴𝐵 is a diameter of a circle with radius 62.5 cm. Point 𝐶 is on the circumference of the circle where 𝐴𝐶𝐶𝐵 and 𝐴𝐶=75cm. Find the exact values of cos𝐴 and sin𝐵.

  • Acos𝐴=35 and sin𝐵=35
  • Bcos𝐴=45 and sin𝐵=45
  • Ccos𝐴=35 and sin𝐵=45
  • Dcos𝐴=45 and sin𝐵=35

Q3:

Find the main trigonometric ratios of 𝐶 given 𝐴𝐵𝐶 is a right-angled triangle at 𝐵 where 20𝐴=21tan.

  • Asin𝐶=2129, cos𝐶=2029 and tan𝐶=2021
  • Bsin𝐶=2129, cos𝐶=2029 and tan𝐶=2120
  • Csin𝐶=2029, cos𝐶=2129 and tan𝐶=2120
  • Dsin𝐶=2029, cos𝐶=2129 and tan𝐶=2021

Q4:

Find the main trigonometric ratios of 𝐴 given 𝐴𝐵𝐶 is a right-angled triangle at 𝐵 where the ratio between 𝐴𝐵 and 𝐴𝐶 is 45.

  • Asin𝐴=35, cos𝐴=45, tan𝐴=34
  • Bsin𝐴=35, cos𝐴=34, tan𝐴=45
  • Csin𝐴=45, cos𝐴=35, tan𝐴=34
  • Dsin𝐴=34, cos𝐴=45, tan𝐴=35

Q5:

Find sincos𝐶𝐶 given that 𝐴𝐵𝐶 is a right-angled triangle at 𝐵 where 𝐴𝐵=8cm and 𝐴𝐶=17cm.

  • A64255
  • B289120
  • C120289
  • D817

Q6:

In the triangle shown, is the side labeled 𝑦 adjacent to angle 𝜃, opposite angle 𝜃, or the hypotenuse?

  • AAdjacent
  • BHypotenuse
  • COpposite

Q7:

In the triangle shown, would we call the side labeled 𝑧 the hypotenuse, the adjacent side to angle 𝜃, or the side opposite angle 𝜃?

  • AThe adjacent side to angle 𝜃
  • BThe side opposite angle 𝜃
  • CThe hypotenuse

Q8:

In the figure, which of the following words describes the position of the side labeled 𝑥 with respect to the angle 𝜃?

  • AOpposite
  • BAdjacent
  • CHypotenuse

Q9:

Find the value of 2𝑋𝑋sincos given 𝑋𝑌𝑍 is a right-angled triangle at 𝑌 where 𝑋𝑌=10cm and 𝑋𝑍=26cm.

  • A120169
  • B169120
  • C2413
  • D1310

Q10:

𝐴𝐵𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=17cm and 𝐵𝐶=30cm. Find the value of tan𝐶𝐴𝐷 given 𝐷 lies on the midpoint of 𝐵𝐶 where 𝐴𝐷𝐵𝐶.

  • A815
  • B1517
  • C158
  • D1715

Q11:

Find 17𝐵𝐶𝐶+𝐵tancossincos, given that 𝐴𝐵𝐶𝐷 is an isosceles trapezoid, where 𝐴𝐷𝐵𝐶, 𝐴𝐷=8cm, 𝐴𝐵=17cm, and 𝐵𝐶=24cm.

Q12:

Find the value of 3𝐶+𝐵tansin, given that 𝐴𝐷𝐵𝐶, 𝐴𝐶=35cm, 𝐷𝐶=28cm, and 𝐴𝐵=29cm.

  • A402145
  • B116345
  • C3910
  • D345116

Q13:

Find the value of sincos𝐵+𝐶.

  • A65
  • B1225
  • C85
  • D75

Q14:

What is the value of tan𝜃 in the given triangle?

  • A32
  • B23
  • C34
  • D35
  • E43

Q15:

Find sin𝐴 and tan𝐴 given 𝐴𝐵𝐶 is a right-angled triangle at 𝐵 where 2𝐶𝐵=𝐴𝐶.

  • Asin𝐴=32 and tan𝐴=33
  • Bsin𝐴=32 and tan𝐴=12
  • Csin𝐴=12 and tan𝐴=33
  • Dsin𝐴=12 and tan𝐴=32

Q16:

What is the value of cos𝜃 in the given triangle?

  • A135
  • B512
  • C1312
  • D513
  • E1213

Q17:

What is the value of sin𝜃 in the given triangle?

  • A1+2
  • B2
  • C1
  • D2
  • E22

Q18:

𝐴𝐵𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=10cm and 𝐵𝐶=16cm. Find the value of sin𝐶𝐴𝐷 given that 𝐷 is the midpoint of 𝐵𝐶.

  • A53
  • B45
  • C35
  • D54

Q19:

Find cos𝐵, given 𝐴𝐵𝐶 is a right-angled triangle at 𝐶 where 𝐴𝐵=17cm and 𝐵𝐶=15cm.

  • A1517
  • B817
  • C1715
  • D178

Q20:

What is the value of cos𝜃 in the given triangle?

  • A35
  • B45
  • C54
  • D53
  • E34

Q21:

Find the value of 2𝐴1sin given 𝐴𝐵𝐶 is a right triangle at 𝐵 where 𝐵𝐶=10cm and 𝐴𝐶=26cm.

  • A169119
  • B119169
  • C119169
  • D4772

Q22:

Find cos𝐴, given 𝐴𝐵𝐶 is a right-angled triangle at 𝐶 where 𝐴𝐵=10cm and 𝐵𝐶=6cm.

  • A45
  • B35
  • C54
  • D53

Q23:

Find the value of tansincos𝐶𝐶𝐶 given 𝐴𝐵𝐶 is a right-angled triangle at 𝐴 where tan𝐵=1.

  • A14
  • B12
  • C22
  • D2

Q24:

What is the value of sin𝜃 in the given triangle?

  • A125
  • B1213
  • C513
  • D135
  • E512

Q25:

𝐴𝐵𝐶 is a triangle, where the ratio between its lengths 𝑎, 𝑏, and 𝑐 is 435. Find sin𝐴.

  • A35
  • B45
  • C15
  • D34

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