Worksheet: The Tangent Ratio

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=5420β€²41β€²β€²βˆ˜, 𝛽=3539β€²19β€²β€²βˆ˜
  • B𝛼=5420β€²41β€²β€²βˆ˜, 𝛽=3014β€²18β€²β€²βˆ˜
  • C𝛼=3014β€²18β€²β€²βˆ˜, 𝛽=5420β€²41β€²β€²βˆ˜
  • D𝛼=3539β€²19β€²β€²βˆ˜, 𝛽=5420β€²41β€²β€²βˆ˜

Q2:

𝐴𝐡𝐢 is a right-angled triangle at 𝐡, where 𝐴𝐡=45cm and 𝐡𝐢=68cm. Find the measure of ∠𝐢 giving the answer to the nearest second.

  • A3329β€²43β€²β€²βˆ˜
  • B4126β€²5β€²β€²βˆ˜
  • C5630β€²17β€²β€²βˆ˜
  • D4833β€²55β€²β€²βˆ˜

Q3:

𝐴𝐡𝐢𝐷 is a rhombus where 𝐴𝐢=24cm and 𝐡𝐷=32cm. Find π‘šβˆ π΅π΄πΆ giving the answer to the nearest second.

  • A3839β€²35β€²β€²βˆ˜
  • B592β€²10β€²β€²βˆ˜
  • C3652β€²12β€²β€²βˆ˜
  • D537β€²48β€²β€²βˆ˜

Q4:

𝐴𝐡𝐢 is a right triangle at 𝐡 where 𝐴𝐡=19cm and π‘šβˆ πΆ=54∘. Find the length of 𝐡𝐢 giving the answer to two decimal places.

Q5:

𝐴𝐡𝐢 is a triangle where π΄π·βŸ‚π΅πΆ, π‘šβˆ π΅=5116β€²18β€²β€²βˆ˜, 𝐡𝐢=20cm, and 𝐴𝐷=8cm. Find π‘šβˆ πΆ giving the answer to the nearest second.

  • A5355β€²12β€²β€²βˆ˜
  • B3029β€²40β€²β€²βˆ˜
  • C1650β€²56β€²β€²βˆ˜
  • D364β€²48β€²β€²βˆ˜

Q6:

The following figure represents a line segment joining two points 𝐴(2,0) and 𝐡(3,8). Find the measure of the angle πœƒ included between 𝐴𝐡 and the π‘₯-axis giving the answer to the nearest second.

  • A7557β€²50β€²β€²βˆ˜
  • B8252β€²30β€²β€²βˆ˜
  • C6926β€²38β€²β€²βˆ˜
  • D2633β€²54β€²β€²βˆ˜

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 𝐴𝐡𝐢 is an equilateral triangle, where point 𝐷 lies on 𝐴𝐡, 𝐴𝐷=5cm, 𝐷𝐡=12cm, and 𝐾𝑋=√3tan.

  • A1217
  • B1712
  • C611
  • D116

Q9:

Find π‘₯ to two decimal places.

Q10:

In the given figure, π‘šβˆ π΅π΄πΆ=90∘ and 𝐴𝐷βŠ₯𝐡𝐢. What isπ΄πΆπœƒtan?

  • A𝐡𝐢
  • B𝐴𝐷
  • C𝐢𝐷
  • D𝐷𝐡
  • E𝐴𝐡

Q11:

𝐴𝐡𝐢 is a right-angled triangle at 𝐡, where 𝐴𝐡=64cm. Point 𝐷 lies on 𝐡𝐢 and point 𝐸 lies on 𝐴𝐢 where 𝐸𝐷βˆ₯𝐴𝐡. Find the length of 𝐷𝐡 given 𝐢𝐷=12cm and 𝐸𝐷=35cm. Give the answer to two decimal places.

Q12:

𝐴𝐡𝐢 is a right triangle at 𝐡 where π‘šβˆ πΆ=3412β€²βˆ˜ and 𝐡𝐢=25cm. Find the length of 𝐴𝐡 giving the answer to two decimal places.

Q13:

Find the exact value of tan𝐢.

  • A49
  • B94
  • C54
  • D45

Q14:

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

  • A3948β€²20β€²β€²βˆ˜
  • B7557β€²50β€²β€²βˆ˜
  • C142β€²10β€²β€²βˆ˜
  • D4717β€²26β€²β€²βˆ˜

Q15:

π‘‹π‘Œπ‘ is a triangle where 𝐿 lies on 𝑋𝑍 such that π‘ŒπΏβŸ‚π‘‹π‘, tantan𝑍=π‘‹π‘ŒπΏ=2021 and 𝑍𝐿=26cm. Find the area of π‘‹π‘Œπ‘ giving the answer to two decimal places.

Q16:

Find the length of 𝐷𝐢 given 𝐴𝐡𝐢𝐷 is a quadrilateral where 𝐴𝐷=6cm and 𝐴𝐡=8cm.

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

Q17:

𝐴𝐡𝐢 is a triangle where π΄π·βŸ‚π΅πΆ, 𝐴𝐷=16cm, π‘šβˆ π΅=44∘, and π‘šβˆ πΆ=48∘. Find, to the nearest centimeter, the length of 𝐡𝐢.

Q18:

In the given figure, π‘šβˆ π΅π΄πΆ=90∘ where 𝐴𝐷βŠ₯𝐡𝐢. What is π΄π·πœƒtan?

  • A𝐴𝐡
  • B𝐴𝐷
  • C𝐴𝐢
  • D𝐡𝐢
  • E𝐡𝐷

Q19:

Find the value of tantanπ‘₯+𝑦 given 𝐴𝐡𝐢𝐷 is a square where points 𝐸 and 𝑂 lie on 𝐴𝐢, 𝐴𝐸=2cm, 𝐸𝑂=13cm, and 𝑂𝐢=1cm.

  • A138
  • B5324
  • C5328
  • D5221

Q20:

𝐴𝐡𝐢 is a right-angled triangle at 𝐡. Point 𝐷 lies on 𝐡𝐢 and point 𝐸 lies on 𝐴𝐢 where 𝐸𝐷βˆ₯𝐴𝐡. Find the area of the trapezoid 𝐴𝐡𝐷𝐸 given 𝐴𝐡=24cm, 𝐢𝐷=35cm, and 𝐸𝐷=12cm. Give the answer to two decimal places.

Q21:

Find the value of tantan𝐡𝐢 given 𝐴𝐡𝐢 is an isosceles triangle where 𝐴𝐡=𝐴𝐢=45cm and 𝐡𝐢=72cm.

  • A916
  • B649
  • C1516
  • D169

Q22:

𝐴𝐡𝐢 is a triangle where 𝑏=11√2π‘Ž and π‘šβˆ πΆ=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 tanπœƒ for △𝐴𝐡𝐢. Give your answer as a fraction in its simplest form.

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

Work out the value of tanπœƒ 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 tanπœƒ for two similar triangles?

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

Q24:

𝐴𝐡 is a diametre of a circle with radius 17 cm. Point 𝐢 is on the circumference of the circle where 𝐴𝐢βŠ₯𝐢𝐡 and 𝐴𝐢=16cm. Find the exact values of tan𝐴 and tan𝐡.

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

Q25:

Find the value of tantan𝑋+𝑍, given π‘‹π‘Œπ‘ is a right-angled triangle at π‘Œ where π‘‹π‘Œ=12cm and 𝑋𝑍=15cm giving the answer to two decimal places.

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