Lesson Worksheet: The Tangent Ratio Mathematics

In this worksheet, we will practice finding an angle in a right triangle using the tangent ratio.


Find the values of 𝛼 and 𝛽 giving your answer to the nearest second.

  • A𝛼=542041, 𝛽=353919
  • B𝛼=542041, 𝛽=301418
  • C𝛼=301418, 𝛽=542041
  • D𝛼=353919, 𝛽=542041


𝐴𝐵𝐶 is a right-angled triangle at 𝐵, where 𝐴𝐵=45cm and 𝐵𝐶=68cm. Find the measure of 𝐶 giving the answer to the nearest second.

  • A332943
  • B41265
  • C563017
  • D483355


𝐴𝐵𝐶𝐷 is a rhombus where 𝐴𝐶=24cm and 𝐵𝐷=32cm. Find 𝑚𝐵𝐴𝐶 giving the answer to the nearest second.

  • A383935
  • B59210
  • C365212
  • D53748


𝐴𝐵𝐶 is a right triangle at 𝐵 where 𝐴𝐵=19cm and 𝑚𝐶=54. Find the length of 𝐵𝐶 giving the answer to two decimal places.


𝐴𝐵𝐶 is a triangle where 𝐴𝐷𝐵𝐶, 𝑚𝐵=511618, 𝐵𝐶=20cm, and 𝐴𝐷=8cm. Find 𝑚𝐶 giving the answer to the nearest second.

  • A535512
  • B302940
  • C165056
  • D36448


The following figure represents a line segment joining two points 𝐴(2,0) and 𝐵(3,8). Find the measure of the angle 𝜃 included between 𝐴𝐵 and the 𝑥-axis giving the answer to the nearest second.

  • A755750
  • B825230
  • C692638
  • D263354


A flagpole 5.9 meters tall casts a 2.8-meter shadow. Find the angle of inclination of the sun giving the answer to the nearest minute.

  • A2820
  • B6140
  • C6437
  • D2523


Find the value of 𝐾, given 𝐴𝐵𝐶 is an equilateral triangle, where point 𝐷 lies on 𝐴𝐵, 𝐴𝐷=5cm, 𝐷𝐵=12cm, and 𝐾𝑋=3tan.

  • A1217
  • B1712
  • C611
  • D116


Find 𝑥 to two decimal places.


In the given figure, 𝑚𝐵𝐴𝐶=90 and 𝐴𝐷𝐵𝐶. What is𝐴𝐶𝜃tan?

  • A𝐵𝐶
  • B𝐴𝐷
  • C𝐶𝐷
  • D𝐷𝐵
  • E𝐴𝐵

This lesson includes 31 additional questions and 291 additional question variations for subscribers.

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