Question

In right triangle abc, ∠a is a right angle, m∠b=44∘, and ac=10. What is the measurement of bc?

Option 1: Approximately 6.95
Option 2: Approximately 7.19
Option 3: Approximately 9.66
Option 4: None of the above

Answer 1

To find the length of BC in triangle ABC, we can use the Pythagorean theorem. Substituting the given values into the equation, we find that BC is approximately 6.95.

Step-by-step explanation:

To find the length of BC in triangle ABC, we can use the Pythagorean theorem, which relates the length of the legs of a right triangle to the hypotenuse. In this case, we have a right triangle with angle B measuring 44 degrees and AC measuring 10. Let's call BC as x. Using the Pythagorean theorem equation, a² + b² = c², we can substitute the given values into the equation to solve for x:

a² + b² = c²

10² + x² = (BC)²

x² = (BC)² - 100

x ≈ √((BC)² - 100)

Since angle B is 44 degrees, we know that BC is the side opposite angle B. Therefore, angle B is the hypotenuse and x is the side opposite angle B. So, BC ≈ √((BC)² - 100). By solving this equation with a calculator, we find that option 1 is the closest approximation, with a value of approximately 6.95.