# The lengths of tw

Consider a triangle ABC with AB = 10 cm, AC = 8 cm and

BAC = 40°

Draw perpendicular from C on AB, say CH.

From right angles triangle ABC,

CH = CA × sin 40°

CH = 8 × sin 40°

(From the table, sin 40° = 0.642 )

CH = 5.136 cm

Area (Δ ABC) = 25.68 cm2

If given angle is 140° i.e. BAC = 140°

Draw perpendicular from C on AB and extend AB to meet it at H.

CH HB

HB is a straight line.

⇒ ∠ HAB = HAC + BAC = 180°

HAC + 140° = 180°

HAC = 40°

In right triangle CHA,

HAC = 40° and AC = 8 cm

CH = CA × sin 40°

CH = 8 × sin 40°

(From the table, sin 40° = 0.642 )

CH = 5.136 cm

Area (Δ ABC) = 25.68 cm2

Hence, Area is same only the position of perpendicular line was changed if the angle is considered as 140°.

Area of triangle (given angle is 40°) = 25.68 cm2 and area of triangle ( angle is taken as 140° ) = 25.68 cm2.

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