Calculate the value of x using the sine rule.
12 cm
7 cm
x°
Answer (1)
To find the value of x using the sine rule, we assume we are dealing with a triangle where two sides and an angle are known, and we want to find another angle or side.
The sine rule is expressed as:
sin A a = sin B b = sin C c
Where a , b , and c are the lengths of the sides of a triangle, and A , B , and C are the angles opposite these sides respectively.
In the given scenario, let's assume:
Side a = 12 cm, and side b = 7 cm.
x is opposite to the side 12 cm.
As there is no direct angle mentioned, let's assume we have angle B opposite 7 cm.
Assuming we know the angle B , we can use the sine rule to solve for angle A (opposite the side a = 12 cm):
sin A 12 = sin B 7
Rearrange the formula to find sin A :
sin A = 7 12 ⋅ sin B
If ∠ B is known, substitute its sine value to calculate sin A and then find ∠ A using the inverse sine function.
If ∠ B is not known, additional information is required to solve the problem, such as the angle value or another side length in the triangle.
