Final answer:
To solve for x in a right triangle where cos B = 2x - 0.52 and sin C = x + 0.24, we equate the two expressions and solve for x, resulting in x = 0.76.
Step-by-step explanation:
To solve for x when given cos B and sin C in a right triangle ABC, we can use the relationship between the cosine of one angle and the sine of another angle in a right triangle. Specifically, since B and C are complementary (their angles sum to 90 degrees), cos B = sin C. Therefore, we can equate the two expressions given:2x - 0.52 = x + 0.24To solve for x, we'll subtract x from both sides and add 0.52 to both sides:x - 0.52 + 0.52 = x + 0.24 + 0.52x = 0.76Thus, x is equal to 0.76.