In triangle ABC given, SinA = 1/3, SinB = 3/4, b = 15cm, find a.
To find side a, we can use the Law of Sines. This law states that the ratio of the length of a side to the sine of its opposite angle is constant in any triangle. In other words, a/sinA = b/sinB = c/sinC.
From sinA = 1/3, we can rearrange the equation to solve for a:
a = sinA * b
a = (1/3) * 15
a = 5 cm
Therefore, side a is 5 cm.
To find side a of triangle ABC, we can use the Law of Sines, which states that the ratio of the length of each side of a triangle to the sine of its opposite angle is constant.
The Law of Sines can be written as:
a / SinA = b / SinB = c / SinC
Given that SinA = 1/3, SinB = 3/4, and b = 15 cm, we can substitute these values into the Law of Sines to obtain:
a / (1/3) = 15 / (3/4)
To simplify the equation, we can multiply both sides by 3:
3a = 15 / (3/4)
Next, we can divide both sides by 3 to isolate a:
a = (15 / (3/4)) / 3
Simplifying this further, we can multiply the numerator and denominator of the fraction by 4/3:
a = (15 * (4/3)) / 3
Now, we can simplify the expression:
a = 60 / 9
Finally, we can divide 60 by 9 to find the value of a:
a = 6.67 cm (rounded to two decimal places)
Therefore, side a of triangle ABC is approximately 6.67 cm.