Mathematics 0580 · IGCSE · Right-angled triangles

Right-angled triangles — practice question

The sketch represents right-angled triangle $ABC$. Here $AB = (2x + 5)\text{ cm}$ and $AC = (x + 3)\text{ cm}$. The right angle is at $A$.

(a(i))[3]

Show that the result is $2x^2 + 11x - 105 = 0$.

(a(ii))[3]

Solve by factorisation. $2x^2 + 11x - 105 = 0$.

(a(iii))[3]

Calculate the angle $ACB$.

(b(i))[1]

Find the measure of the smallest angle in triangle $DEF$.

(b(ii))[3]

Find the length of the smallest side of triangle $DEF$.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Setting up $(x+3)(2x+5)/2=60$” …