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Lesson Worksheet: Right Triangle Trigonometry: Solving for a Side Mathematics

In this worksheet, we will practice finding the value of a missing side length in a right triangle by choosing the appropriate trigonometric ratio for a given angle.

Q1:

Find 𝑥 to two decimal places.

Q2:

Find the length of 𝐵𝐶 giving the answer to two decimal places.

Q3:

𝐴𝐵𝐶 is an isosceles triangle where 𝐴𝐵=𝐴𝐶=9cm, 𝐴𝐷𝐵𝐶 and 𝑚𝐶=34. Find the length of 𝐵𝐶 giving the answer to one decimal place.

Q4:

Find 𝑥 to two decimal places.

Q5:

In the figure 𝐴𝐶=3.5.

What is 𝐴𝐵? Give your answer to two decimal places.

Q6:

Find the values of 𝑥 and 𝑦 giving the answer to three decimal places.

  • A𝑥=38.285cm, 𝑦=26.110cm
  • B𝑥=47.432cm, 𝑦=38.285cm
  • C𝑥=26.110cm, 𝑦=38.285cm
  • D𝑥=38.285cm, 𝑦=47.432cm

Q7:

𝐴𝐵𝐶 is a right-angled triangle at 𝐵 where 𝑚𝐶=62 and 𝐴𝐶=17cm. Find the lengths of 𝐴𝐵 and 𝐵𝐶 giving the answer to two decimal places and the measure of 𝐴 giving the answer to the nearest degree.

  • A𝐴𝐵=15.01cm, 𝐵𝐶=7.98cm, 𝑚𝐴=28
  • B𝐴𝐵=7.98cm, 𝐵𝐶=15.01cm, 𝑚𝐴=38
  • C𝐴𝐵=15.01cm, 𝐵𝐶=7.98cm, 𝑚𝐴=38
  • D𝐴𝐵=7.98cm, 𝐵𝐶=15.01cm, 𝑚𝐴=28

Q8:

𝐴𝐵𝐶𝐷 is a rhombus where the side length is 28 m and 𝑚𝐴𝐵𝐶=1296. Find the lengths of the diagonals giving the answer to three decimal places.

  • A𝐴𝐶=12.032cm, 𝐵𝐷=58.835cm
  • B𝐴𝐶=24.065cm, 𝐵𝐷=50.566cm
  • C𝐴𝐶=50.566cm, 𝐵𝐷=24.065cm
  • D𝐴𝐶=50.566cm, 𝐵𝐷=117.671cm
  • E𝐴𝐶=117.671cm, 𝐵𝐷=24.065cm

Q9:

A kite, which is at a perpendicular height of 44 m, is attached to a string inclined at 60 to the horizontal. Find the length of the string accurate to one decimal place.

Q10:

A 23 ft ladder leans against a building such that the angle between the ground and the ladder is 80. How high does the ladder reach up the side of the building? Give your answer to two decimal places.

This lesson includes 34 additional questions and 243 additional question variations for subscribers.

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