Shape and Space 4

4 marks · Normal

Triangle ABC is right-angled at B. AB = 6.2 cm and AC = 11.5 cm. Calculate, giving your answers to 3 significant figures,

(a)

(a) the length BC

[2 marks]

(b)

(b) the size of angle BAC

[2 marks]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) 9.76 cm

(b) 57.9 degrees

Common mistakes: Mixing up sides; Using sine instead of cosine for the angle

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Correct application of Pythagoras' theorem to find BC

A1 (a) · 1 mark · Correct value for BC (to 3 s.f.) (follow-through)

M1 (b) · 1 mark · Correct trigonometric set-up for angle BAC (using cosine or sine rule) (follow-through)

A1 (b) · 1 mark · Correct value for angle BAC (to 1 d.p. or 3 s.f.) (follow-through)

Worked solution

Let BC = x.

Angle BAC is adjacent/hypotenuse so use cosine: