Lesson Worksheet: Trigonometric Ratios in Right Triangles Mathematics • 10th Grade

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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 that 𝐴𝐵𝐶 is a right 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:

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

  • A64255
  • B289120
  • C120289
  • D817

Q3:

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

  • A402145
  • B116345
  • C3910
  • D345116

Q4:

Find the main trigonometric ratios of ∠𝐴, given that 𝐴𝐵𝐶 is a right triangle at 𝐵, where the ratio between 𝐴𝐵 and 𝐴𝐶 is 4∶5.

  • 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 sin𝐴 and tan𝐴, given that 𝐴𝐵𝐶 is a right triangle at 𝐵, where 2𝐶𝐵=𝐴𝐶.

  • Asin𝐴=√32, tan𝐴=√33
  • Bsin𝐴=√32, tan𝐴=12
  • Csin𝐴=12, tan𝐴=√33
  • Dsin𝐴=12, tan𝐴=√32

Q6:

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

Q7:

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

  • A120169
  • B169120
  • C2413
  • D1310

Q8:

𝐴𝐵 is a diameter of a circle with radius 62.5 cm. Point 𝐶 is on the circumference of the circle where 𝐴𝐶⟂𝐶𝐵 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

Q9:

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

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

Q10:

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

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