Name: Trigonometric Ratios for the Angle of 30 Degrees
Uploaded: 2019-07-19
Duration: 3 min 17 s
Description: What is the angular bisector of 60 degrees? It is 30 degree. Wondering how? Let us learn the trigonometric ratios of 30 degree in this interesting video!

Question

The given triangles $A B C, D E F$ and $G H I$ have measures $3 - 4 - 5, 6 - 8 - 10$ and $12 - 16 - 20$ . Are they all right triangles?
How do you know? The angles at the vertices $B, E$ and $H$ are of equal size (each angle is equal to $θ$ ).

With these available details, fill up the following table and comment on the ratios that you get.

In $△ A B C$	In $△ D E F$	In $△ G H I$
$\sin θ = \frac{3}{5}$	$\sin θ = \frac{6}{10} = \frac{3}{5}$	$\sin θ = \frac{12}{20} = ?$
$\cos θ =$ ?	$\cos θ =$ ?	$\cos θ =$ ?
$\tan θ = \frac{3}{4}$	$\tan θ =$ ?	$\tan θ =$ ?

.

Accepted Answer

From the given,

The given triangles are $A B C, D E F$ and $3 - 4 - 5, 6 - 8 - 10$ are right triangles.

We can apply Pythagoras theorem to verify whether a triangle is right triangle

${(hypotenuse)}^{2} = {(opposite side)}^{2} + {(adjacent side)}^{2}$

$Δ A B C \Rightarrow (3, 4, 5) \Rightarrow 3^{2} + 4^{2} = 25 = 5^{2}$

$Δ D E F \Rightarrow (6, 8, 10) \Rightarrow 6^{2} + 8^{2} = 100 = 10^{2}$

$∆ G H I \Rightarrow (12, 16, 20) \Rightarrow 12^{2} + 16^{2} = 400 = 20^{2}$

We know, $sinθ = \frac{opposite side}{hypotenuse}, cosθ = \frac{adjacent side}{hypotenuse}, Tanθ = \frac{opposite side}{adjacent side}$

In $△ ABC$ In $△ DEF$ In $△ GHI$

$\sin θ = \frac{3}{5}$ $\sin θ = \frac{6}{10} = \frac{3}{5}$ $\sin θ = \frac{12}{20} = \frac{3}{5}$

$\cos θ = \frac{4}{5}$ $\cos θ = \frac{8}{10} = \frac{4}{5}$ $\cos θ = \frac{16}{20} = \frac{4}{5}$

$\tan θ = \frac{3}{4}$ $\tan θ = \frac{6}{8} = \frac{3}{4}$ $\tan θ = \frac{12}{16} = \frac{3}{4}$

Hence, we can say the given are the right- angled triangles because trigonometric ratios are equal in similar triangles.

Important Questions on Trigonometry

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