Geoimeatraidh

Gus faid taoibh air triantan ceart-cheàrnach obrachadh a-mach nuair a tha fios agad air meud an dà thaoibh eile, feumaidh tu Teoraidh Phythagoras a chleachdadh.

A rèir Teoraidh Phythagoras, ann an triantan ceart-cheàrnach:

Tha faid cheàrnagaichte a' hypotenuse co-ionann ri sùim faidean ceàrnagaichte an dà thaoibh eile.

Pythagoras diagram showing right angled triangle with values a, b and c and squares a≤, b≤ and c≤

Tha e nas fhasa seo a sgrìobhadh mar:

{a^2} = {b^2} + {c^2}

Diagram of right angled triangle with a, b and c dimensions and the formula a² = b² + c²

Ag obrachadh a-mach faid a' hypotenuse

Question

Cleachd Teoraidh Phythagoras agus obraich a-mach faid a' hypotenuse. Thoir do fhreagairt gu 2 ionad deicheach.

rectangle 4 x 7 x X

Sgrìobh an co-aontar x^{2} = 7^{2} + 4^{2}

Ceàrnagaich na faidean as aithne dhut x^{2} = 49 + 16

Cuir-ris x^{2} = 65

Obraich a-mach am freumh ceàrnagach x = \sqrt {65}

x = 8.06 \,(gu\,2\,id.)

Question

Obraich a-mach faid taobh x

Thoir do fhreagairt gu 2 ionad deicheach.

Diagram of a 5 x 9 right-angled triangle with the gradient edge marked x

x^{2} = 5^{2} + 9^{2}

x^{2} = 25 + 81

x^{2} = 106

x = \sqrt {106}

x = 10.30 \,(gu\,2\,id.)

Eisimpleir

Obraich a-mach faid taobh a.

Thoir do fhreagairt gu 2 ionad deicheach.

rectangle 12 x 8 x a

Freagairt

  • Sgrìobh an co-aontar: {12^2} = {a^2} + {8^2}
  • Cuir air dòigh an co-aontar {a^2} = {12^2} - {8^2}. Gus faid taobh goirid obrachadh a-mach, faodaidh sinn cuideachd am foirmle {b^2} = {a^2} - {c^2} a chleachdadh.
  • Ceàrnagaich na faidean as aithne dhut: {a^2} = 144 - 64
  • Dèan thoir-air-falbh: {a^2} = 80
  • Obraich a-mach am freumh ceàrnagach: a = \sqrt {80}
  • a = 8.94 \,(gu\,2\,id.)

Question

Obraich a-mach faid taobh a.

Thoir do fhreagairt gu 2 ionad deicheach.

Right-angled triangle with values a, 9 and 13

a^{2} = 13^{2} - 9^{2}

a^{2} = 169 - 81

a^{2} = 88

a = \sqrt 88

a = 9.38