Ceàrnan ann an leth-chearcall

Nuair a thèid triantan a chruthachadh ann an leth-chearcall, bidh dà loidhne bho gach taobh dhen trast-thomhas a' coinneachadh aig puing air a' chearcall-thomhas aig ceàrn ceart.

Diagram of a right-angled scalene triangle within a circle

'S e ceàrn ceart de \(90^\circ\) a tha sa cheàrn ann an leth-chearcall.

Question

San diagram, 's e trast-thomhas a th' ann am PR agus tha \(\angle PRQ = 25^\circ\)

Dè am meud a th' ann an \(\angle QPR\)?

Diagram of a right-angled scalene triangle within a circle, the R angle is 25°

Tha \(\angle PQR = 90^\circ\) oir 's e ceàrn ann an leth-cheacall a th' ann.

Tha na trì ceàrnan ann an triantan a' tighinn gu \(180^\circ\), agus mar sin:

\[\angle QPR = 180^\circ - 90^\circ - 25^\circ\]

\[\angle QPR = 65^\circ\]
Question

San diagram tha KL na thrast-thomhas dhen chearcall agus tha e 8 cm a dh'fhaid.

LM = 3 cm.

Obraich a-mach meud KM.

Diagram of a right-angled scalene triangle within a circle, dimensions 8cm x 3cm x unknown

Tha KL na thrast-thomhas agus tha ceàrn againn ann an leth-chearcall. Mar sin tha \(\angle KML = 90^\circ\).

Tha triantan ceart-cheàrnach againn agus faodaidh sinn mar sin Pythagoras a chleachdadh.

Chan e KM a' hypotenuse agus mar sin:

\[K{M^2} = {8^2} - {3^2} = 55\]

\[KM = \sqrt {55} = 7.461...\]

\[KM = 7.4\,cm\,(gu\,1\,id.)\]