The length of the hypotenuse of the given triangle = 6
What do we mean by trigonometric ratios?
The values of all trigonometric functions dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides with regard to any of its acute angles are known as that angle's trigonometric ratios.
The three sides of the right triangle are:
Hypotenuse (the longest side)
Perpendicular (opposite side to the angle)
Base (Adjacent side to the angle)
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
The trigonometry ratios for a specific angle ‘θ’ is given below:
Trigonometric Ratios:
Sin θ Perpendicular/Hypotenuse
Cos θ Base/Hypotenuse
Tan θ Perpendicular/Base or Sin θ/Cos θ
Cot θ Base/Perpendicular or 1/tan θ
Sec θ Hypotenuse/Base or 1/cos θ
Cosec θ Hypotenuse/Perpendicular or 1/sin θ
How do we solve the given question?
In the given diagram, Let the triangle be ABC with ∠A = 30°, ∠B = 90°, and ∠C = 60°.
∴ The hypotenuse is AC, the Perpendicular is BC, and the Base is AB with respect to ∠A.
Taking sine of ∠A, we get
sin A = Perpendicular/Hypotenuse
or, sin 30° = BC/AC
or, 1/2 = 3/AC (∵ sin 30° = 1/2)
or, AC = 6
∴ The length of the hypotenuse of the given triangle = 6
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