First assume that it is possible to construct such a triangle.

If ∠ABC = 90°, then △ABC is a right-angled triangle.

This means that AC is the hypotenuse since it is the side directly opposite the right angle.

AB = 6cm, BC = 8cm (given)


Since given that ∠ACB = 35°,

Then tan∠ACB = opposite/adjacent

= AB/BC
= 6cm/8cm
= 3/4 or 0.75

But tan∠ACB = tan35°
= 0.700 (3 s.f)

And 0.700 ≠ 0.75

So this results in a contradiction

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Another way to show :

If ∠ACB = 35° and ∠ABC = 90°,

Then by the sine rule,

AC / sin 90° = AB / sin ∠ACB

AC / 1 = 6 cm / sin 35°

AC = 10.46 cm (4 s.f)

But if ∠ABC is right-angled,

Then by Pythagoras' Theorem,

AB² + BC² = AC²
(6cm)² + (8cm)² = AC²
36cm² + 64cm² = AC²
100cm² = AC²
AC = √100 cm
= 10cm ≠ 10.46cm

This also results in a contradiction