What is the length of the adjacent side of this right-angled triangle, relative to a) the $71^{\circ}$ angle? b) the $19^{\circ}$ angle? Not drawn accurately Values given are approximate

Step 1 ：Given a right-angled triangle with one angle being $71^\circ$ and another angle being $19^\circ$. We need to find the length of the adjacent side relative to both angles. Since we are not given any side lengths, we can assume the hypotenuse to be of length 1 unit (as it will not affect the ratio of the sides).

Step 2 ：We can use the trigonometric function cosine to find the length of the adjacent side relative to both angles.

Step 3 ：For the $71^\circ$ angle, the adjacent side will be the side that is not the hypotenuse and not opposite to the angle. We can use the cosine function to find the length of this side: \(\text{Adjacent side length} = \cos(71^\circ)\)

Step 4 ：For the $19^\circ$ angle, the adjacent side will be the side that is not the hypotenuse and not opposite to the angle. We can use the cosine function to find the length of this side: \(\text{Adjacent side length} = \cos(19^\circ)\)

Step 5 ：\(\text{Adjacent side length relative to } 71^\circ \approx 0.326\)

Step 6 ：\(\text{Adjacent side length relative to } 19^\circ \approx 0.946\)

Step 7 ：\(\boxed{\text{Final Answer:}}\)

Step 8 ：a) The length of the adjacent side relative to the $71^\circ$ angle is approximately 0.326 units.

Step 9 ：b) The length of the adjacent side relative to the $19^\circ$ angle is approximately 0.946 units.