Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )

Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )

Tangent ratio is yet another trigonometric ratio for right-angled triangles. Tangent ratio is the ratio of opposite side to adjacent side of a right triangle. Same as the sine and cosine ratios, tangent ratios can be used to calculate the angles and sides of right angle triangles.

Lessons

  • 1.
    What are sine, cosine and tangent?

  • 2.
    Determine each tangent ratio using calculator
    i) tan70\tan 70^\circ
    ii) tan134\tan-134^\circ

  • 3.
    Determine the angle to the nearest degree
    i) tanθ=0.64\tan \theta = 0.64
    ii) tanθ=1.45\tan \theta = -1.45

  • 4.
    Determine the angles and sides using Tangent
    a)
    Find angle A and B:

    Use tangent ratio and side lengths of triangle to calculate angles

    b)
    Find the value of "x" using tangent

    Use tangent ratio, adjacent side and tangent theta to calculate opposite side length

    c)
    Find the value of "x" using tangent

    Use tangent ratio, adjacent side length and tangent theta to calculate opposite side length


  • 5.
    Draw and label a right triangle to illustrate tangent ratio, then calculate the angle.
    a)
    tanθ=59\tan \theta = {5 \over 9}