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Question
In ΔABC, ∠B = 90°, AB = 3 cm, AC = 6 cm, then θ = ______.
Options
30°
45°
60°
none of these
MCQ
Fill in the Blanks
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Solution
In ΔABC, ∠B = 90°, AB = 3 cm, AC = 6 cm, then θ = 60°.
Explanation:
To find the value of θ in the right-angled triangle ABC, the cosine trigonometric ratio can be used, which is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
`cos(theta) = "Adjacent"/"Hypotenuse" = (AB)/(AC)`
`cos(theta) = 3/6 = 1/2`
To find the angle θ, the inverse cosine function is used:
`theta = cos^(-1) (1/2)`
The value of the angle whose cosine is `1/2` is 60°.
Therefore, θ = 60°.
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