Point (2,3) is on a circle with the center (3,5). What is the radius of the circle?
2 answers:
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Answer: We can find angle BAC by using (1) SinA = 9.8/12
(2) CosA = 6.9/12
(3) TanA = 9.8/6.9
Step-by-step explanation: The question indicates that we have a right angled triangle ABC with the right angle at point C (that is, angle ACB is the right angle). Also the three sides have been labeled as AB equals 12 cm, CB equals 9.8 cm and AC equals 6.9 cm. Line AB has been identified as the hypotenuse and angle A (that is, BAC) is the reference angle. If angle A is the reference angle, then line CB facing angle A shall be the opposite side, while line AC is the adjacent (which lies between the reference angle and the right angle). Please see the attached diagram for details.
Having these details available, we can actually find angle A by using any of the three trigonometric ratios, since all three sides are given. Hence,
SinA = opposite/hypotenuse
SinA = 9.8/12
SinA = 0.8167
Checking with your calculator or table of values, A = 54.76 (approximately 55)
Also CosA = adjacent/hypotenuse
CosA = 6.9/12
CosA = 0.5750
Checking with your calculator or table of values A = 54.90 (approximately 55).
Finally TanA = opposite/adjacent
TanA = 9.8/6.9
TanA = 1.4203
Checking with your calculator or table of values A = 54.83 (approximately 55).
