Question

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

∠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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Answer 2

Answer:

Refer to the images below :)