In the triangle, the length of side a is 5 ft, and m<A=60°. Find the exact lengths of sides b and c. What would the answer be?
To find the lengths of sides b and c, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
Let's denote the length of sides b and c as b and c, respectively. We know that the length of side a is 5 ft, and the measure of angle A is 60°.
Using the Law of Sines, we have:
a/sin(A) = b/sin(B) = c/sin(C)
Substituting the given values, we get:
5/sin(60°) = b/sin(B) = c/sin(C)
Since sin(60°) = √3/2, we have:
5/(√3/2) = b/sin(B) = c/sin(C)
Multiplying both sides of the equation by √3/2, we get:
(5√3/2) = b/sin(B) = c/sin(C)
Simplifying, we obtain:
(5√3/2) = b/sin(B) = c/sin(C)
To find the exact lengths of sides b and c, we need additional information such as the measure of angle B or C or the lengths of another side. Without this information, we cannot determine the exact lengths of sides b and c.
Therefore, the answer cannot be determined based on the given information.