Question

If tan 0 = 5/12 and 0 is acute, find the values of sin 0 and cos 0.

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Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

If tan Ф = 5/12 & Ф is acute angle.

$\underline{\bf{Explanation\::}}$

Firstly, attachment a figure of right angled Δ according to the question.

So,

$\boxed{\sf {tan\theta = \dfrac{Perpendicular}{Base}} }$

$\mapsto\tt{tan \theta = \dfrac{5}{12} = \dfrac{BC}{AB} }$

$\underline{\mathcal{USING\:PYTHTAGORAS\:THEOREM\::}}$

→ (Hypotenuse)² = (Base)² + (Perpendicular)²

→ (AC)² = (AB)² + (BC)²

→ (AC)² = (12)² + (5)²

→ (AC)² = 144 + 25

→ (AC)² = 169

→ AC = √169

→ AC = 13 unit

Now,

• sin Ф

$\mapsto\tt{sin\:\theta = \dfrac{Perpendicular}{Hypotenuse} }$

$\mapsto\tt{sin\:\theta = \dfrac{BC}{AC} }$

$\mapsto\tt{sin\:\theta = \dfrac{5}{13} }$

• cos Ф

$\mapsto\tt{cos\:\theta = \dfrac{Hypotenuse}{Perpendicular} }$

$\mapsto\tt{cos\:\theta = \dfrac{AC}{BC} }$

$\mapsto\tt{cos\: \theta = \dfrac{13}{5} }$

Answer 2

Question :-

If tan 0 = 5/12 and 0 is acute, find the values of sin 0 and cos 0.

Given :-

Tan ϑ = 5/12

Have to find :-

Sin ϑ = ?

Cos ϑ = ?

Solution :-

As we all know the trigonometry ratios :-

Sin ϑ =

$\frac{perpendicular}{hypotense}$

Cos ϑ =

$\frac{base}{hypotense}$

Tan ϑ =

$\frac{perpendicular}{base}$

Hence ,

From given we know that Tan ϑ = 5/12 = Perpendicular/ base

We got ,

P = 5

B = 12

Now , In ∆ ABC

Simply applying the Pythagoras Theorem :-

↠ ( Hypotense ) ² = ( Perpendicular ) ² + ( Base ) ²

↠ ( Hypotense ) ² = ( 5 ) ² + ( 12 ) ²

↠ ( Hypotense ) ² = 25 + 144

↠ ( Hypotense ) ² = 169

↠ ( Hypotense ) = √ 169

↠ ( Hypotense ) = 13

Hence , Now we know the value of sin ϑ and Cos ϑ

So ,

P = 5

B = 12

H = 13

• Sin ϑ

= P/ h

= 5/13

• Cos ϑ

= B / h

= 12/ 13