The length of side BC in the right-angled triangle ABC is calculated using the cosine of angle A, resulting in BC approximately equal to 10.827 cm, which rounded to three significant figures is 10.8 cm.
To calculate the length of side BC in a right-angled triangle ABC where angle B is 90 degrees and angle A is 36 degrees, with AB measuring 8.7 cm, we can use trigonometric functions. Specifically, the cosine of angle A and the adjacent side AB can help us find BC:
cos(A) = adjacent/hypotenuse
=> cos(36°) = AB/BC
=> BC = AB / cos(36°)
Therefore, substituting AB with 8.7 cm:
BC = 8.7 cm / cos(36°)
=> BC ≈ 10.827 cm
When rounded to three significant figures:
BC = 10.8 cm