Question

Please help me! Thank you! I only need help with a)

Answer 1

Since we know AD, CD and angle D, we can use the law of cosines, which states that

$AC^2 = AD^2+CD^2 - 2AD\cdot CD\cos(D)$

Plugging the values, we have

$AC^2 = 17^2+13^2 - 2\cdot 17\cdot 13\cos(42)$

Which leads to

$AC^2 = 458 - 442\cos(42) \approx 129.530$

Taking the square root, we have

$AC \approx \sqrt{129.530} \approx 11.3811$