Question

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Calculate the value of sin 30° using Triangulation method .
Give diagram also. Please answer fast. Exams approaching.

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Answer 1

Answer:-

$\pink{\bigstar}$ Value of sin 30° $\large\leadsto\boxed{\rm\purple{\dfrac{1}{2} \: or \: 0.5}}$

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• Method:-

• Triangulation method

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• Solution:-

Let's consider an equilateral traingle with sides ABC having all sides 60°.

In order to find the value of sin 30 we need to know the length of each sides. Consider, the length of AB = 2a such that half of each is a.

✯ Refer to the figure below.

★ Figure:-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\qbezier(3,3)(3,0)(3,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf B }\put(5.2,-0.3){ \bf C }\put(3.0,-0.4){ \bf D }\put(1.0,1.5){ \bf 2a }\put(1.8,-0.4){ \bf a }\end{picture}$

Here,

Δ ABD ≅ ∆ ACD

Also,

BD = DC and

∠BAD=∠CAD

∆ ABD is a right triangle,

Right-angled at D with ∠BAD=30∘

and ∠ABD=60∘.

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Now, we clearly know this formula,

$\pink{\bigstar}$ $\underline{\boxed{\bf\green{sin \theta = \dfrac{Perpendicular}{Hypotenuse}}}}$

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Here, the Perpendicular is a and Hypotenuse is 2a.

• Substituting in the Formula:-

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➪ $\sf sin \theta = \dfrac{a}{2a}$

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★ $\large{\bf\red{sin \: \theta = \dfrac{1}{2}}}$

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Therefore, the value of sin 30° is 1/2 or 0.5.

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★ Note:- Kindly view from website for clear view of Figure.

Answer 2

Answer:

Question :-

• Calculate the value of sin 30° using triangulation method.
• Give diagram.

To Find :-

• What is the value of sin 30°.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{sin{\theta} =\: \dfrac{Perpendicular}{Hypotenuse}}}}$

Solution :-

$\mapsto$ ∆ ABC is a right angled-triangle.

Let,

$\mapsto$ Perpendicular = x

$\mapsto$ Hypotenuse = 2x

Now, we have to find the sin 30° :-

$\implies \sf sin{\theta} =\: \dfrac{a}{2a}$

$\implies \sf sin{\theta} =\: \dfrac{\cancel{x}}{2\cancel{x}}$

$\implies \sf sin{\theta} =\: \dfrac{1}{2}$

$\implies \sf\bold{\red{sin{\theta} =\: 0.5}}$

$\therefore$ The value of sin 30° is 0.5 .

[ Note :- Please refer the attachment for the diagram. ]

$\rule{150}{2}$

IMPORTANT FORMULA :-

$\diamondsuit$ $\leadsto \sf\boxed{\bold{\pink{cos{\theta} =\: \dfrac{Base}{Hypotenuse}}}}$

$\diamondsuit$ $\leadsto \sf\boxed{\bold{\pink{tan{\theta} =\: \dfrac{Perpendicular}{Base}}}}$

$\diamondsuit$ $\leadsto \sf\boxed{\bold{\pink{cosec{\theta} =\: \dfrac{Hypotenuse}{Perpendicular}}}}$

$\diamondsuit$ $\leadsto \sf\boxed{\bold{\pink{sec{\theta} =\: \dfrac{Hypotenuse}{Base}}}}$

$\diamondsuit$ $\leadsto \sf\boxed{\bold{\pink{cot{\theta} =\: \dfrac{Base}{Perpendicular}}}}$