X = 4cm
y = 6 cm
work out
∠
BAC rounded to 3 SF.

Step-by-step explanation:

I am not sure if I understand you right about what is needed.

I would understand we need the angle BAC (at A).

first of all, this is a right-angled triangle.

Pythagoras applies :

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

in our case that means

AC² = x² + y² = 4² + 6² = 16 + 36 = 52

AC = sqrt(52)

now we can use the law of sine to get the other angles.

a/sin(A) = b/sin(B) = c/sin(C)

with the sides and the corresponding angles being opposite.

in our case

y/sin(A) = AC/sin(B) = AC/sin(90) = AC

sin(A) = y/AC = 6/sqrt(52) = 0.832050294...

the angle A = 56.30993247...° ≈ 56.3°

y= -

1.30

step-by-step explanation: