Question

a ladder 15 metres long just reaches the top of a vertical wall . if the the ladder makes an angle of 60 degree with the wall find the height of the wall

Answer 1

Hi friend
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Your answer
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Length of ladder = 15 m

The ladder reaches the top of a vertical wall.

Angle made by the ladder = 60°

Height of the wall = x = ?


Now,
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sin60° = x/15

=> √3/2 = x/15

=> x = (√3 × 15)/2

=> x = 7.5√3 m

HOPE IT HELPS

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

PQ shows the wall on OQ be the ladder

OQ = 15 m

Also,

∠PQO = 60

Now

In right angle traingle OPQ we have

$\tt{\rightarrow\dfrac{PQ}{OQ}=cos60}$

$\tt{\rightarrow\dfrac{PQ}{OQ}=\dfrac{1}{2}}$

$\tt{\rightarrow PQ=OQ\times\dfrac{1}{2}}$

$\tt{\rightarrow PQ=\dfrac{15}{2}}$

= 7.5 m

Therefore we get :-

Height of wall is 7.5 m

$\boxed{\begin{minipage}{11 cm} Fundamental Trignometric Indentities \\ \\ \tan (90 - A) = cotA \\ \\ cot (90 - A) = tanA \\ \\ sec (90 - A) = cosecA \\ \\ tan\theta =\dfrac{sin\theta}{cos\theta} \\ \\ cot\theta =\dfrac{cos\theta}{sin\theta} \\ \\ cosec (90 - A) = secA \\ \\ sin^{2}\theta+\cos^{2}\theta =1\\ \\ 1+tan^{2}\theta=\sec^{2}\theta \\ \\ 1 + cot^{2}\theta=\text{cosec}^2\theta \end{minipage}}$