Lesson Worksheet: Trigonometric Ratios Mathematics

In this worksheet, we will practice finding and expressing the values of the three trigonometric ratios—sine, cosine, and tangent—for a given angle in a right triangle.

Q1:

Find sin𝐵, given that 𝐴𝐵𝐶 is a right triangle at 𝐶, where 𝐴𝐵=17cm and 𝐵𝐶=15cm.

  • A178
  • B817
  • C1517
  • D1715

Q2:

What is the value of cos𝜃 in the given triangle?

  • A135
  • B512
  • C1312
  • D513
  • E1213

Q3:

A 5 m ladder is leaning against a vertical wall such that its base is 2 m from the wall. Work out the angle between the ladder and the floor, giving your answer to two decimal places.

  • A68.19
  • B23.57
  • C66.42
  • D21.80

Q4:

A car is going down a ramp that is 10 meters high and 71 meters long. Find the angle between the ramp and the horizontal, giving the answer to the nearest second.

  • A815412
  • B812
  • C8548
  • D81548
  • E623142

Q5:

Find 𝑥 to two decimal places.

Q6:

Find 𝑥 to two decimal places.

Q7:

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

Q8:

Given the following figure, find the lengths of 𝐴𝐶 and 𝐵𝐶 and the measure of 𝐵𝐴𝐶 in degrees. Give your answers to two decimal places.

  • A𝐴𝐶=10.23, 𝐵𝐶=9.42, 𝑚𝐵𝐴𝐶=68.00
  • B𝐴𝐶=10.68, 𝐵𝐶=9.90, 𝑚𝐵𝐴𝐶=69.00
  • C𝐴𝐶=10.34, 𝐵𝐶=9.53, 𝑚𝐵𝐴𝐶=70.00
  • D𝐴𝐶=10.68, 𝐵𝐶=9.90, 𝑚𝐵𝐴𝐶=68.00
  • E𝐴𝐶=10.57, 𝐵𝐶=9.78, 𝑚𝐵𝐴𝐶=68.00

Q9:

A kite has a string of length 75 meters. The angle the string makes with the horizontal ground is 53. Find the height of the kite from the ground giving the answer to two decimal places.

Q10:

In the given figure, given that 𝐴𝐶=10 and 𝑚𝐴𝐶𝐵=50, find the lengths of 𝐴𝐵 and 𝐵𝐶 and the measure of 𝐴𝐵𝐶 in degrees. Give your answers to two decimal places.

  • A𝐴𝐵=7.66, 𝐵𝐶=12.60, 𝑚𝐴𝐵𝐶=41.00
  • B𝐴𝐵=6.42, 𝐵𝐶=11.88, 𝑚𝐴𝐵𝐶=40.00
  • C𝐴𝐵=8.39, 𝐵𝐶=13.05, 𝑚𝐴𝐵𝐶=38.00
  • D𝐴𝐵=11.92, 𝐵𝐶=15.56, 𝑚𝐴𝐵𝐶=40.00
  • E𝐴𝐵=11.92, 𝐵𝐶=15.56, 𝑚𝐴𝐵𝐶=42.00

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