Serlo Logo The Open Learning Platform

Exercises: Sine, Cosine and Tangent on a right triangle

  1. 1

    Calculate the missing sides and angles (marked red) of the triangles

    1. γ=90
      a=12.7cm
      c=24.9cm
      Image
    2. α=90
      b=420m
      a=645m
      Image
    3. β=90
      c=15.8cm
      a=30.7cm

      Image
    4. γ=90
      α=35
      c=12.5cm

      Image
    5. α=90
      γ=40.3
      a=10.5cm
      Image
  2. 2

    In a right triangle with a=5 cm and α=75°compute the length of b.

    Rechtwinkliges Dreieck Aufgabe Tangens
  3. 3

    Calculate the missing sides and angles of the isosceles triangle ABC with a=b. Note that we are looking at general isosceles triangles that are not necessarily right-angled.

    1. a=44.2cm

      c=63.4cm

    2. a=114.5m

      α =32.3°

    3. c=35.4cm

      β =43.9°

    4. h=14.8cm

      α=β= 28.3°

    5. a=146.4m

      h=58.4m

  4. 4

    A triangle with a right angle at C, with side b=113m has an angle α=39 . First make a sketch and then calculate all the missing sides and the other angle β .

  5. 5

    Sketch a rectangle with sides a=7cm and b=18cm and calculate the angles

    1. between a diagonal and the sides

    2. between both diagonals

  6. 6

    In a circle with radius r=10cm the chord s has the central angle α=84.

    What is the length of the chord?

  7. 7

    Heike is 1.69m tall. How long is her shadow when the sun's rays hit the ground at an angle of 30°? Give the result in metres rounded to 2 decimal places.

    m
  8. 8

    Calculate the missing sides and angles of the isosceles triangle ABC with a=b.

    1. a = 44.2cm

      c = 63.4cm

    2. a = 114.5m

      α = 32.3°

    3. c = 35.4cm

      β = 43.9°

    4. hc = 14.8cm

      α = 28.3°

    5. a = 146.4m

      hc = 58.4m

  9. 9

    This sketch, which is not to scale, shows a trapezoid with the lengths:

    AD=7m,DAB=DCB=CDA=90,CAD=50,ADE=55

    Calculate the distance of x

    Image
  10. 10

    This sketch, which is not to scale, shows a kite quadrilateral ABCD with symmetry axis AC and the sides: a=7cm, c=6cm, DB=10cm

    Compute the angles α,β and γ.

    Image
  11. 11

    This sketch, which is not to scale, shows a rectangle with side lengths a=5.0cm and b=7.0cm.

    Calculate the angle α.

    Image
  12. 12

    This sketch shows a right triangle, not true to size, with height h=8cm and angles α=65 and β=80.

    Calculate the side lengths a and b.

    a=tan(α)ha=tan(65)8cma=17.16cmb=tan(β)hb=tan(80)8cmb=45.37cm

    Image