In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectivelyTrigonometric RatioIn the first triangle, we need to use trigonometric ratio to find the missing side in the triangleData;Angle = 45hypothenuse = [tex]8\sqrt{2}[/tex]adjacent = xTo find the adjacent side, we need to use cosine rule on this problem.[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]The adjacent side is equal to 8 unitsIn the second triangle, we also need to use trigonometric ratio, but let's write down our dataangle = 30hypothenuse = 10opposite = ?adjacent = ?We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]The adjacent side is equal to 8.660, let's find the opposite side using sine rule[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]And lastly, the value of the other angle is[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectivelyLearn more on trigonometric ratios here;