Lesson Worksheet: The Tangent Ratio Mathematics

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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=5420′41′′∘, 𝛽=3539′19′′∘
  • B𝛼=5420′41′′∘, 𝛽=3014′18′′∘
  • C𝛼=3014′18′′∘, 𝛽=5420′41′′∘
  • D𝛼=3539′19′′∘, 𝛽=5420′41′′∘

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.

  • A3329′43′′∘
  • B4126′5′′∘
  • C5630′17′′∘
  • D4833′55′′∘

Q3:

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

  • A3839′35′′∘
  • B592′10′′∘
  • C3652′12′′∘
  • D537′48′′∘

Q4:

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

Q5:

𝐴𝐵𝐶 is a triangle where 𝐴𝐷⟂𝐵𝐶, 𝑚∠𝐵=5116′18′′∘, 𝐵𝐶=20cm, and 𝐴𝐷=8cm. Find 𝑚∠𝐶 giving the answer to the nearest second.

  • A5355′12′′∘
  • B3029′40′′∘
  • C1650′56′′∘
  • D364′48′′∘

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.

  • A7557′50′′∘
  • B8252′30′′∘
  • C6926′38′′∘
  • D2633′54′′∘

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, 𝑚∠𝐵𝐴𝐶=90∘ and 𝐴𝐷⊥𝐵𝐶. What is𝐴𝐶𝜃tan?

  • A𝐵𝐶
  • B𝐴𝐷
  • C𝐶𝐷
  • D𝐷𝐵
  • E𝐴𝐵

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

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