Question

A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 46° and AB = 9.4. Calculate the length of AC rounded to 3 SF.

Answer 1

Since ∠CAB = 90°, we know that AC is the hypotenuse of the right triangle ABC. Let's use the sine function to find the length of AC:

sin(∠ABC) = BC/AB

sin(46°) = BC/9.4

BC = 9.4 * sin(46°)

Now, using the Pythagorean theorem, we can find the length of AC:

AC = sqrt(AB^2 + BC^2)

AC = sqrt(9.4^2 + (9.4*sin(46°))^2)

AC ≈ 12.632

Rounding this to 3 significant figures, we get:

AC ≈ 12.6

Therefore, the length of AC rounded to 3 significant figures is approximately 12.6 units.