Calculate |AB| and |BC| to the nearest meter.

Question

ScanSolve AI Tutor · Accepted Answer

Here's how to calculate the lengths of sides AB and BC:

Calculate |AB|

Identify the knowns and the side to be found.
We have a right-angled triangle ABC, with the right angle at B.
The hypotenuse AC is $12 \text{ m}$ .
Angle C is $57^\circ$ .
Side AB is opposite to angle C.
Use the sine trigonometric ratio.
The sine of an angle is the ratio of the opposite side to the hypotenuse.
$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}$ $\sin(57^\circ) = \frac{AB}{12}$
Solve for AB.
Multiply both sides by 12.
$AB = 12 \times \sin(57^\circ)$ $AB \approx 12 \times 0.83867$ $AB \approx 10.06404 \text{ m}$
Round to the nearest meter.
$AB \approx 10 \text{ m}$
The length of AB is $\boxed{10 \text{ m}}$ .

Calculate |BC|
Identify the knowns and the side to be found.
We have a right-angled triangle ABC.
The hypotenuse AC is $12 \text{ m}$ .
Angle C is $57^\circ$ .
Side BC is adjacent to angle C.
Use the cosine trigonometric ratio.
The cosine of an angle is the ratio of the adjacent side to the hypotenuse.
$\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}$ $\cos(57^\circ) = \frac{BC}{12}$
Solve for BC.
Multiply both sides by 12.
$BC = 12 \times \cos(57^\circ)$ $BC \approx 12 \times 0.54464$ $BC \approx 6.53568 \text{ m}$
Round to the nearest meter.
$BC \approx 7 \text{ m}$
The length of BC is $\boxed{7 \text{ m}}$ .

Step-by-step solution