Answer:
Step-by-step explanation:
Answer:
The exact value of sin(45) is √22.
Step-by-step 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.