Pythagoras: finding a shorter side

The Maths Habit

  1. Find c.

    c = 65 cm

  2. Find c to 1 decimal place.

    c = 12.5 cm

  3. Find c.

    c = 7.4 m

What is the same? What is different?

What is the value of a?

  1. a + 3 = 8

    a = 5

  2. a + 4.6 = 10

    a = 5.4

  3. a + 4.75 = 11.3

    a = 6.55

  4. a2 + 36 = 100

    a = 8

x2 =252 − 202x2 =625 − 400x2 =225x =√225 = 15 cm
x2 =342 − 162x2 =1156 − 256x2 =900x =√900 = 30 cm
x2 =252 − 202x2 =625 − 400x2 =225x =√225 = 15 cm

Give your answer to 1 decimal place.

x2 =132 − 62x2 =169 − 36x2 =133x =√133 = 11.532…= 11.5 cm
x2 =252 − 202x2 =625 − 400x2 =225x =√225 = 15 cm
x2 =172 − 82x2 =289 − 64x2 =225x =√225 = 15 cm
x2 =252 − 202x2 =625 − 400x2 =225x =√225 = 15 cm

Give your answer to 1 decimal place.

x2 =142 − 92x2 =196 − 81x2 =115x =√115 = 10.723…= 10.7 cm
x2 =252 − 202x2 =625 − 400x2 =225x =√225 = 15 cm
x2 =7.52 − 4.52x2 =56.25 − 20.25x2 =36x =√36 = 6 m

Pythagoras: finding a shorter side worksheet, page 1

Pythagoras: finding a shorter side worksheet, page 2

Answer sheet

  1. A zip wire 65 m long runs from the top of a tower to the ground. It lands 63 m from the foot of the tower. How tall is the tower?

    16 m

  2. An isosceles triangle has two sides of 13 cm and a base of 10 cm. How tall is the triangle?

    12 cm

  1. Find the length x.

    x = 15 cm
    x8 cm17 cm

  2. Find the length x to 1 decimal place.

    x = 10.9 cm
    x5 cm12 cm

  3. The triangle is isosceles. Find its height, h.

    h = 15 cm
    16 cm17 cm17 cmh
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