Question

Class 10

Mathematics

Chapter 9 - Some applications of Trigonometry

Formulas Needed

Quality Answer Needed​

Answer 1

Their aren't any formulas in chapter 'some application of trignometry' but you should be aware of the important terms from this chapter and Trignometry ratios and formula.

~Important Terms!!

• Line of sight:-

the line of sight is a line drawn from the eye of an observer to the point in the object viewed by the observer.

• angle of elevation:-

the angle of elevation of an object viewed, is the angle formed by the line of sight with the horizontal level when it's above the horizontal level.

• angle of depression:-

the angle of depression of an object viewed, is the angle formed by the line of sight with the horizontal level is below the horizontal level.

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$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}</p><p><strong><u>----------------------------------------------------</u></strong></p><p></p><p>[tex] \sf{⇝sin\theta= \frac{perpendicular}{hypothenuse}}$

$\sf{⇝cos\theta =\frac{Base}{hypothenuse} }$

$\sf{⇝sin\theta= \frac{perpendicular}{hypothenuse}}$

$\sf{⇝tan\theta = \frac{perpendicular}{base}}$

$\sf{⇝cosec\theta = \frac {hypothenuse}{perpendicular}}$

$\sf{⇝sec\theta = \frac{hypothenuse}{Base}}$

$\sf{⇝Cot\theta = \frac{base}{perpendicular}}$

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Answer 2

$\huge{\underline{\underline{\bf Required\:Answer}}}$

• The formulas for "Applications of Trigonometry and "Trigonometric Ratios" are same.

Basic Formula:-

For a triangle ABC, (attachment) , the trigonometric ratios for Ø are as follows:-

$\implies\sf \sin(\theta) = \dfrac{opposite \: side}{hypotenues} = \frac{AB}{AC} \\ \\ \implies\sf\cos(\theta) = \dfrac{adjacent \: side}{hypotenues} = \frac{BC}{AC} \\ \\ \implies\sf \tan(\theta) = \dfrac{opposite \: side}{adjacent \: side} = \frac{AB}{BC} \\ \\ \implies\sf \csc(\theta) = \dfrac{1} { \sin(\theta) } = \dfrac{hypotenues}{opposite \: side} = \frac{AC}{AB} \\ \\ \implies\sf \sec(\theta) = \dfrac{1}{ \cos(\theta) } = \dfrac{hypotenues}{adjacent \: side} = \frac{AC}{BC} \\ \\ \sf \implies\cot(\theta) = \dfrac{1}{ \tan(\theta) } = \frac{adjacent \: side}{opposite \: side} = \frac{BC}{AB}$

Trigonometric Ratios for standard angles

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}$

Some more important Formula for tan and Cot

$\sf \implies \tan(\theta) = \dfrac{ \sin(\theta) }{ \cos(\theta) } \\ \\ \implies \cot(\theta) = \frac{ \cos(\theta) }{ \sin(\theta) }$

Important Identies:-

$\sf \implies { \sin^{2}(\theta) } + { \ \cos ^{2}(\theta) } = 1 \\ \\ \implies{ \ \sec ^{2}(\theta) } - { \ \tan ^{2}(\theta) } = 1 \\ \\ \implies{ \ \csc ^{2}(\theta) } - { \ \cot ^{2}(\theta) } = 1$

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