Question

in a. triangle the value adjacent opposite and hypotenuse sides are given find the unknown variable​

Answer 1

Answer:

a) Side BC = 6$\sqrt{3}$ cm , b) side PR = 2$\sqrt{7}$ cm , side MO =  $\sqrt{7}$ cm

Step-by-step explanation:

Given : Three right angled triangles, we can apply pythogorous therom to

             find third side.

a) Triangle  ABC,

    AB= 6 cm, AC= 12 cm, BC = x cm

∴ AC² = AB² + BC²

   12² = 6² + x²

    x² = 12² - 6²

        = 144 - 36

        = 108

        = 36 x 3

    x = $\sqrt{36 x 3}$

       = 6$\sqrt{3}$ cm

b) In triangle PRQ, PQ = 8 cm, QR = 6 cm and PR = y cm

∴ PQ² = PR² + QR²

  8² = y² + 6²

  y² = 8² - 6²

      = 64 - 36

      = 28

      = 7 x 4

  y = $\sqrt{7 X 4}$

     = 2$\sqrt{7}$ cm

c) In triangle MON, MN = 4cm, MO = z cm and ON = 3 cm

∴ MN² = MO² + ON²

     4² = z² + 3²

     z² = 4² - 3²

         =16 - 9

         = 7

     z = $\sqrt{7}$ cm