In Fig. 9.5, AT is a tangent to the circlewith centre O such that OT = 4 cmand ∠OTA = 30°. Then AT is equal to
Question
In Fig. 9.5, AT is a tangent to the circlewith centre O such that OT = 4 cmand ∠OTA = 30°. Then AT is equal to
Solution
The problem you're describing is a trigonometry problem involving a right triangle. Here's how you can solve it:
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Identify the right triangle: In this case, the right triangle is OTA, with OT being the adjacent side and AT being the opposite side of the angle ∠OTA.
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Use the tangent of the angle to find the length of AT: The tangent of an angle in a right triangle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, tan(30°) = AT/OT.
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Substitute the given values into the equation: tan(30°) = AT/4 cm.
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Solve for AT: AT = 4 cm * tan(30°).
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Calculate the value: The tangent of 30 degrees is √3/3, so AT = 4 cm * √3/3 = 4√3/3 cm.
So, the length of AT is 4√3/3 cm.
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