Which scenarios involves right triangles?
2 answers:
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One thing to pay close attention to is that, AB is a segment whose length is 12 cm, now we're not referring to the arcAB, but to the straight-line going from A to B, the segment AB, as you can see in the picture below in green.
now, the segments OA and OB are radius of the circle and therefore twins, and since they're twin sides, they make up twin angles on the other end, the green end.
if those angles at A and B are twins, the only possible values for them is 60°, what the dickens does all that mean?
well, it means the triangle AOB is an equilateral triangle, and if AB is 12, then OA and OB are also twelve, thus we know the radius of the circle is 12.
now, that is the circumference of that circle, and since we only need to know what arcAB is, and since arcAB is 1/6 of the circle, then 1/6 of that circumference is 24π/6.
now, the segments OA and OB are radius of the circle and therefore twins, and since they're twin sides, they make up twin angles on the other end, the green end.
if those angles at A and B are twins, the only possible values for them is 60°, what the dickens does all that mean?
well, it means the triangle AOB is an equilateral triangle, and if AB is 12, then OA and OB are also twelve, thus we know the radius of the circle is 12.
now, that is the circumference of that circle, and since we only need to know what arcAB is, and since arcAB is 1/6 of the circle, then 1/6 of that circumference is 24π/6.
The values of sin (x/2) = 4/√17, cos (x/2) = 1/√17 and tan (x/2) = 4.
<h3>What is Trigonometry?</h3>Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.
Here, cos x = -15/17 (given)
we know, cos x = 2cos²x/2 - 1
cos²(x/2) = (cos x + 1)/2
cos²(x/2) = (-15/17 + 1)/2
cos²(x/2) = 1/17
cos (x/2) = 1/√17
then, sin (x/2) = √(1- cos²(x/2))
sin (x/2) = √(1 - 1/17)
sin (x/2) = √16/17
sin (x/2) = 4/√17
and tan (x/2) = sin (x/2) / cos (x/2)
tan (x/2) =
tan (x/2) = 4
Thus, the values of sin (x/2) = 4/√17, cos (x/2) = 1/√17 and tan (x/2) = 4.
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