Which of the following triangles cannot be solved using the sine law?
a) angle a= 28 degrees, angle b= 75 degrees, side a= 24 cm
b) side a=4 cm , side b= 11 cm
c) angle a=28 degrees, angle c= 34 degrees , side b=5 cm
d) angle b= 29 degrees, side b=5 cm, side c=18 cm
(b) no angles provided
Not
In order to determine which of the triangles cannot be solved using the sine law, we need to check if we have enough information to apply the law.
The sine law states that for any triangle, the ratio of a side length to the sine of the opposite angle is the same for all three sides. Mathematically, it can be represented as:
a/sin(A) = b/sin(B) = c/sin(C)
Now let's analyze each option:
a) angle a = 28 degrees, angle b = 75 degrees, side a = 24 cm
In this case, we have both angle a and angle b, as well as side a. We can apply the sine law since we have enough information.
b) side a = 4 cm, side b = 11 cm
In this case, we do not have any angles given. Without any angle measurements, we cannot apply the sine law. Therefore, option b cannot be solved using the sine law.
c) angle a = 28 degrees, angle c = 34 degrees, side b = 5 cm
In this case, we have both angle a and angle c, as well as side b. We can apply the sine law since we have enough information.
d) angle b = 29 degrees, side b = 5 cm, side c = 18 cm
In this case, we only have one angle, angle b, and two side lengths, side b and side c. We do not have enough information to apply the sine law since we don't have any other angle measurement. Therefore, option d cannot be solved using the sine law.
In summary, the triangles that cannot be solved using the sine law are option b) and option d).
To determine which triangle cannot be solved using the sine law, we need to check if we have enough information to apply the sine law equation.
The sine law states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. This can be expressed by the formula:
a/sin(A) = b/sin(B) = c/sin(C)
Let's go through the given triangles and see if they can be solved using the sine law:
a) angle a = 28 degrees, angle b = 75 degrees, side a = 24 cm
To solve this triangle, we would need either the length of side b or the measure of angle B. However, we don't have that information, so this triangle cannot be solved using the sine law.
b) side a = 4 cm, side b = 11 cm
To solve this triangle, we would need either the measure of angle A or angle B. However, we don't have any information about the angles, so this triangle cannot be solved using the sine law.
c) angle a = 28 degrees, angle c = 34 degrees, side b = 5 cm
In this triangle, we have the measure of both angle A and angle C, as well as the length of side b. Therefore, we can use the sine law to solve this triangle.
d) angle b = 29 degrees, side b = 5 cm, side c = 18 cm
In this triangle, we have the measure of angle B, side b, and side c. Therefore, we can use the sine law to solve this triangle.
So, the triangles that cannot be solved using the sine law are options a) and b).