Question

Help meee!!!
im so stuck and cant figure this out

Answer 1

The length of side AB is 8.856cm

To find the length of side AB in a triangle with angle C measuring 41° and side AC measuring 13.5 cm, we can use the trigonometric sine ratio. The sine ratio is defined as:

`\[ \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} \]`

In this case, side AB is the opposite side to angle C, and side AC is the hypotenuse. Therefore:

`\[ \sin(41°) = \frac{AB}{13.5 \, \text{cm}} \]`

To find side AB, rearrange the equation:

`\[ AB = 13.5 \, \text{cm} * \sin(41°) \]`

Now, plug in the values and calculate:

`\[ AB \approx 13.5 \, \text{cm} * \sin(41°) \]\\AB \approx 13.5 \, \text{cm} * 0.656059 \]\\AB \approx 8.85598 \, \text{cm} \]`

Rounding to three significant figures, the length of side AB is approximately
`\(8.86 \, \text{cm}\)`. The given answer of
`\(8.856 \, \text{cm}\)` is very close and might be rounded differently.