Question

A, B & C form the vertices of a triangle.

∠
CAB = 90°,
∠
ABC = 47° and AB = 8.8.
Calculate the length of BC rounded to 3 SF.

Answer 1

12.903

Explanation:

You want the measure of BC in right triangle ABC with A=90°, B=47° and AB=8.8.

Trig relations

The relations between sides and trig functions of the angles in a right triangle are summarized by the mnemonic SOH CAH TOA. Useful here is the relation between the side adjacent to the given acute angle and the hypotenuse:

Cos = Adjacent/Hypotenuse

cos(47°) = AB/BC

Solution

Solving for BC, we get ...

BC = AB/cos(47°) = 8.8/cos(47°)

The calculator (2nd attachment) shows this to be ...

BC = 12.903