Calculate the length of sides labelled in the circles below. The lines AB and AC are tangents.
Problem 1 :
Solution :
Using Pythagorean theorem :
(OA)^{2} = (OB)^{2} + (AB)^{2}
x^{2} = (5)^{2} + (12)^{2}
x^{2} = 25 + 144
x^{2} = 169
x = 13
So, the value of x is13 cm.
Calculate
the length of sides labelled in the circles below. The lines AB and AC are
tangents.
Problem 2 :
Solution :
Using Pythagorean
theorem :
(AO)^{2} = (AB)^{2} + (OB)^{2}
(20)^{2} = (x)^{2} + (8)^{2}
400 = x^{2} + 64
x^{2} = 400 - 64
x^{2} = 336
x = 18.330
So, the value of x is18.330 cm.
Problem 3 :
Solution :
Using Pythagorean
theorem :
OA^{2} = AC^{2} + OC^{2}
30^{2} = 20^{2} + x^{2}
900 = 400 + x^{2}
x^{2} = 900 - 400
x^{2} = 500
x = 10√5
So, the value of x is 22.36 cm.
Calculate the size of x in the circles below. The lines AB and AC are tangents.
Problem 4 :
Solution :
sin x = opposite/hypotenuse
= BO/AO
= 6/13
sin x = 0.4615
x = sin ^{-1} (0.4615)
= 27.48
So, the angle is 27.48.
Problem 5 :
Solution :
sin x = opposite/hypotenuse
x = AB/AO
= 12/15
sin x = 0.8
x = sin^{-1} 0.8
= 53.13
So, the angle is 53.13.
Problem 6 :
Solution :
cos 25^{º} = adjacent/hypotenuse
0.9063 = x/20
x = 0.9063 × 20
x = 18.126
So, the missing side is 18.126 cm.
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