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

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 ∠𝐡 given that 𝐴𝐡𝐢 is a right triangle at 𝐢, where 𝐴𝐡=30cm and 𝐡𝐢=18cm.

  • Asin𝐡=35, cos𝐡=45, tan𝐡=43
  • Bsin𝐡=45, cos𝐡=35, tan𝐡=43
  • Csin𝐡=35, cos𝐡=45, tan𝐡=34
  • Dsin𝐡=45, cos𝐡=35, tan𝐡=34

Q2:

Find sincos𝐢𝐢 given that 𝐴𝐡𝐢 is a right triangle at 𝐡, where 𝐴𝐡=8cm and 𝐴𝐢=17cm.

  • A64255
  • B289120
  • C120289
  • D817

Q3:

Find the value of 3𝐢+𝐡tansin, given that π΄π·βŸ‚π΅πΆ, 𝐴𝐢=35cm, 𝐷𝐢=28cm, and 𝐴𝐡=29cm.

  • A402145
  • B116345
  • C3910
  • D345116

Q4:

Find the main trigonometric ratios of ∠𝐴, given that 𝐴𝐡𝐢 is a right triangle at 𝐡, where the ratio between 𝐴𝐡 and 𝐴𝐢 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 𝐴𝐡𝐢 is a right triangle at 𝐡, where 2𝐢𝐡=𝐴𝐢.

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

Q6:

𝐴𝐡𝐢 is an isosceles triangle where 𝐴𝐡=𝐴𝐢=10cm and 𝐡𝐢=16cm. Find the value of sin𝐢𝐴𝐷 given that 𝐷 is the midpoint of 𝐡𝐢.

  • A53
  • B45
  • C35
  • D54

Q7:

Find the value of 2𝑋𝑋sincos given that π‘‹π‘Œπ‘ is a right triangle at π‘Œ, where π‘‹π‘Œ=10cm and 𝑋𝑍=26cm.

  • A120169
  • B169120
  • C2413
  • D1310

Q8:

𝐴𝐡 is a diameter of a circle with radius 62.5 cm. Point 𝐢 is on the circumference of the circle where π΄πΆβŸ‚πΆπ΅ and 𝐴𝐢=75cm. Find the exact values of cos𝐴 and sin𝐡.

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

Q9:

Find the main trigonometric ratios of ∠𝐢 given that 𝐴𝐡𝐢 is a right triangle at 𝐡, where 20𝐴=21tan.

  • Asin𝐢=2129, cos𝐢=2029, tan𝐢=2021
  • Bsin𝐢=2129, cos𝐢=2029, tan𝐢=2120
  • Csin𝐢=2029, cos𝐢=2129, tan𝐢=2120
  • Dsin𝐢=2029, cos𝐢=2129, tan𝐢=2021

Q10:

Find 17𝐡𝐢𝐢+𝐡tancossincos, given that 𝐴𝐡𝐢𝐷 is an isosceles trapezoid, where 𝐴𝐷βˆ₯𝐡𝐢, 𝐴𝐷=8cm, 𝐴𝐡=17cm, and 𝐡𝐢=24cm.

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