Lesson Worksheet: The Tangent Ratio Mathematics

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

Q1:

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

Q2:

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

Q3:

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

  • A383935
  • B59210
  • C365212
  • D53748

Q4:

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.

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

Find 𝑥 to two decimal places.

Q10:

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.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.