Worksheet: The Tangent Ratio

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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

Q11:

𝐴𝐵𝐶 is a right-angled triangle at 𝐵, where 𝐴𝐵=64cm. Point 𝐷 lies on 𝐵𝐶 and point 𝐸 lies on 𝐴𝐶 where 𝐸𝐷∥𝐴𝐵. Find the length of 𝐷𝐵 given 𝐶𝐷=12cm and 𝐸𝐷=35cm. Give the answer to two decimal places.

Q12:

𝐴𝐵𝐶 is a right triangle at 𝐵 where 𝑚∠𝐶=3412′∘ and 𝐵𝐶=25cm. Find the length of 𝐴𝐵 giving the answer to two decimal places.

Q13:

Find the exact value of tan𝐶.

  • A49
  • B94
  • C54
  • D45

Q14:

The dimensions of a rectangular yard is 13 meters by 12 meters. Triangle 𝐴𝐸𝐶 represents the lawn where 𝐸𝐶=10m. Find the measure of ∠𝐸𝐴𝐵 giving the answer to the nearest second.

  • A3948′20′′∘
  • B7557′50′′∘
  • C142′10′′∘
  • D4717′26′′∘

Q15:

𝑋𝑌𝑍 is a triangle where 𝐿 lies on 𝑋𝑍 such that 𝑌𝐿⟂𝑋𝑍, tantan𝑍=𝑋𝑌𝐿=2021 and 𝑍𝐿=26cm. Find the area of 𝑋𝑌𝑍 giving the answer to two decimal places.

Q16:

Find the length of 𝐷𝐶 given 𝐴𝐵𝐶𝐷 is a quadrilateral where 𝐴𝐷=6cm and 𝐴𝐵=8cm.

  • A445 cm
  • B1313 cm
  • C10 cm
  • D712 cm

Q17:

𝐴𝐵𝐶 is a triangle where 𝐴𝐷⟂𝐵𝐶, 𝐴𝐷=16cm, 𝑚∠𝐵=44∘, and 𝑚∠𝐶=48∘. Find, to the nearest centimeter, the length of 𝐵𝐶.

Q18:

In the given figure, 𝑚∠𝐵𝐴𝐶=90∘ where 𝐴𝐷⊥𝐵𝐶. What is 𝐴𝐷𝜃tan?

  • A𝐴𝐵
  • B𝐴𝐷
  • C𝐴𝐶
  • D𝐵𝐶
  • E𝐵𝐷

Q19:

Find the value of tantan𝑥+𝑦 given 𝐴𝐵𝐶𝐷 is a square where points 𝐸 and 𝑂 lie on 𝐴𝐶, 𝐴𝐸=2cm, 𝐸𝑂=13cm, and 𝑂𝐶=1cm.

  • A138
  • B5324
  • C5328
  • D5221

Q20:

𝐴𝐵𝐶 is a right-angled triangle at 𝐵. Point 𝐷 lies on 𝐵𝐶 and point 𝐸 lies on 𝐴𝐶 where 𝐸𝐷∥𝐴𝐵. Find the area of the trapezoid 𝐴𝐵𝐷𝐸 given 𝐴𝐵=24cm, 𝐶𝐷=35cm, and 𝐸𝐷=12cm. Give the answer to two decimal places.

Q21:

Find the value of tantan𝐵𝐶 given 𝐴𝐵𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=45cm and 𝐵𝐶=72cm.

  • A916
  • B649
  • C1516
  • D169

Q22:

𝐴𝐵𝐶 is a triangle where 𝑏=11√2𝑎 and 𝑚∠𝐶=45∘. Find the value of tan𝐴 without using a calculator.

  • A121√2
  • B21
  • C121
  • D√221

Q23:

In the given figure, the two triangles are similar.

Work out the value of tan𝜃 for △𝐴𝐵𝐶. Give your answer as a fraction in its simplest form.

  • A1112
  • B√26511
  • C1211
  • D12√265265
  • E11√265265

Work out the value of tan𝜃 for △𝐷𝐸𝐹. Give your answer as a fraction in its simplest form.

  • A√26512
  • B1211
  • C12√265265
  • D1112
  • E11√265265

What can be said about the value of tan𝜃 for two similar triangles?

  • AThey will never be equal.
  • BThey are always equal.
  • CThey are often equal.

Q24:

𝐴𝐵 is a diametre of a circle with radius 17 cm. Point 𝐶 is on the circumference of the circle where 𝐴𝐶⊥𝐶𝐵 and 𝐴𝐶=16cm. Find the exact values of tan𝐴 and tan𝐵.

  • Atan𝐴=817, tan𝐵=158
  • Btan𝐴=158, tan𝐵=815
  • Ctan𝐴=158, tan𝐵=817
  • Dtan𝐴=815, tan𝐵=158

Q25:

Find the value of tantan𝑋+𝑍, given 𝑋𝑌𝑍 is a right-angled triangle at 𝑌 where 𝑋𝑌=12cm and 𝑋𝑍=15cm giving the answer to two decimal places.

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