The above links to a question in the 2019 IGCSE maths 0580 specimen paper.
I know the answer is $75$, and have been able to figure this out logically, namely $$\frac{35}{7} \times 8 = 40 + 35 = 75.$$ However the answer paper seems to suggest this can be answered using "correct trig or Pythagoras’ method leading to value rounding to 40.0". I am a bit stumped by this as I don't see how...any help appreciated.
On
It can also be solved using similarity of triangles The triangle having base of 8 cm is similar to the triangle having base of 15 cm . The hypotenuse of the smaller triangle will be $l-35$ and and that of the larger triangle would be $l$ thus by using properties of similarity of triangles we get $$ \frac{8}{l-35} = \frac{15}{l} $$ $$ 8l = 15l -525 $$ $$7l =525 $$ $$ l=75 $$
Obviously either the question meant to ask about just the length of the dotted line segment, or the person supplying the answer thought the question was about that segment rather than the whole line labeled $\ell$.