3. In triangle ABC right angled at B, BC = 3 cm and AC – AB = 1 cm.
Determines the value of sin A, sin C and cosec A and cot C.
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Answer:
sinA = 0.6
sin C = 0.8
cosec A = 5/3
cot C = 0.75
Step-by-step explanation:
As the triangle is right angled at B, therefore, AC is the hypotenuse, and AB and BC are its other 2 sides.
AC - AB = 1
AB = AC - 1
By Pythagoras theorem,
(Base)^2 + (Height)^2 = (Hypotenuse)^2
(3)^2 + (AC - 1)^2 = AC^2
9 + AC^2 + 1 - 2AC = AC^2
(We eliminate AC^2 on both sides)
9 + 1 = 2AC
AC = 5 cm
AB = AC - 1 = 4 cm
sin A = Opposite/Hypotenuse = BC/AC = 3/5
sinA = 0.6
sin C = Opposite/Hypotenuse = AB/AC = 4/5
sin C = 0.8
cosec A = 1 / sin A
cosec A = 5/3
cot C = Adjacent/Opposite = BC/AB = 3/4
cot C = 0.75
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