Find the value of the function for θ. sin(45°) = ? i need the explanation if possible. possible answers below.

Step-by-step explanation:

The exact value of sin(45) is √22.

Explanation:

Consider △ABC to be right-angled in B and choose ∠BCA such that its measure is 45o. Since the triangle is isosceles, we can deduce that angle ∠CAB is also 45o. Then pick an arbitrary value for AB and BC and apply the Pythagorean theorem. I'll go with the unit triangle, choosing both AB and BC to be 1 (remember, the triangle is isosceles):

The hypothenuse AC can easily be calculated now: AC=√BC2+AB2=√12+12=√2.

The sine is defined as the ratio between the opposed side and the hypothenuse. Therefore, sin45o=1√2=√22.

In decimal form, it is roughly 0.7071067812.

1. Set up a ratio: 3/2.25 = 4/x

Cross multiply:

3x = 2.25*4

3x = 9

Divide both sides by 3:

x = 9/3

x = 3

2. Set up a ratio: 12/2x+1 = 8/x+4

Cross multiply:

12(x+4) = 8(2x+1)

Simplify:

12x +48 = 16x +8

Subtract 8 from each side:

12x +40 = 16x

Subtract 12x from each side:

40 = 4x

Divide both sides by 4:

x = 40/4

X = 10

3. Find the ratio of the smaller triangle to the larger triangle: using the two ends: 15 /5 = 3

The larger triangle is 3 times larger than the smaller one.

Because the two given angles are on opposite sides, this means the sides of the triangle are mirrored so X is the equivalent of side 8 times the ratio:

x = 8 *3 = 24