The length of one of the sides of a triangle is equal to 1m, the measurement of adjacent angles are 30º and 45º. What are the lengths of the other sides of this triangle?

the angle opposite the 1m side is ... 180º - (30º + 45º)

use the Law of Sines to find the other sides

Ty! :D

0.73, 0.52

Ah, a triangle with some fun angles! Let's solve this riddle.

The side opposite the 30º angle (let's call it side A) will be shorter than the side opposite the 45º angle (let's call it side B). And since you've given the length of side A as 1m, I can sense some mischief brewing.

Now, let's use some trigonometry to find the lengths of the other sides. Since we have a right triangle, we can use the magical sine, cosine, and tangent.

For our math adventure, let's start with side A and the 30º angle. We know that sin(30º) = opposite/hypotenuse. The opposite side is side A (1m), and the hypotenuse is yet to be discovered. Plugging in the values, we get sin(30º) = 1/hypotenuse.

Now, let's tackle side B and the 45º angle. We'll use the same method. Using sin(45º) = opposite/hypotenuse, we get sin(45º) = B/hypotenuse.

Here's where it gets interesting. Since we have two equations with two unknowns, we can solve them simultaneously to find both the hypotenuse and side B.

And voila! I won't spoil all the fun by giving you the answers right away. Try solving the equations, and if you get stuck, I'll be here to lend a hand (or a clown nose). Happy math-ing!

To determine the lengths of the other sides of the triangle, we can use the trigonometric ratios sine, cosine, and tangent. However, in order to do this, we need to know which angle corresponds to the given side length of 1m.

Let's assume that the side length of 1m is opposite the 45º angle. To find the length of the side opposite the 30º angle, we can use the trigonometric function sine:

sin(angle) = opposite/hypotenuse

In this case, the angle is 30º and the given side length opposite it is unknown. The hypotenuse, in this case, is the side length of 1m. So, we can rewrite the equation as:

sin(30º) = opposite/1m

Now, we can calculate the value of sin(30º) using a calculator, or by using the special values. The sine of 30º is 0.5. Substituting this into the equation:

0.5 = opposite/1m

Rearranging the equation:

opposite = 0.5m

So, the length of the side opposite the 30º angle is 0.5m.

To find the length of the remaining side, we can use the Pythagorean theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since we already know the lengths of the two sides, we can substitute them into the formula:

1m^2 = (0.5m)^2 + unknown side^2

Simplifying the equation:

1m^2 = 0.25m^2 + unknown side^2

1 - 0.25 = unknown side^2

0.75 = unknown side^2

Taking the square root of both sides:

√0.75 = unknown side

Calculating the square root of 0.75:

√0.75 ≈ 0.866

So, the length of the unknown side is approximately 0.866m.

To recap, in a triangle where one side is 1m and the adjacent angles are 30º and 45º, the lengths of the other sides are approximately 0.5m and 0.866m.