Question

The length of one of the sides of a triangle is 1 m, and the measures of the adjacent angles are 30 and 45. five exact answers for the lengths of the other sides of the triangle.

Answer 1

To find the lengths of the other sides of the triangle, we can use trigonometric ratios. The lengths are: 0.5 m, 0.96 m, 0.87 m, 0.71 m, and 0.58 m.

Step-by-step explanation:

First, let's use the information given to draw a triangle. We know that one side of the triangle is 1 m and the adjacent angles are 30 degrees and 45 degrees. The sum of all angles in a triangle is 180 degrees. Since we know 2 angles, we can find the third angle by subtracting their sum from 180 degrees:

Third angle = 180 degrees - (30 degrees + 45 degrees)

Third angle = 180 degrees - 75 degrees

Third angle = 105 degrees

Now, we can use the trigonometric ratios to find the lengths of the other sides of the triangle:

Sine (sin) ratio:

Sin(30 degrees) = Opposite/hypotenuse

Sin(30 degrees) = x/1 m

x = 1 m * Sin(30 degrees)

x = 0.5 m

Similarly, we can find the lengths of the other sides:

x = 1 m * Sin(105 degrees)

x = 0.96 m

x = 1 m * Cos(30 degrees)

x = 0.87 m

x = 1 m * Cos(45 degrees)

x = 0.71 m

x = 1 m * Tan(30 degrees)

x = 0.58 m