Question

A ladder 5 meter long, leans against a wall. It makes an angle of 60 degree with the horizontal ground. Calculate how far up the wall the ladder reaches

Answer 1

$\red{{ \bf GIVEN :}}$

• Height of ladder = 9 m
• Angle of elevation = 60°

$\bf </strong><strong> </strong><strong>\</strong><strong>b</strong><strong>l</strong><strong>u</strong><strong>e</strong><strong>{</strong><strong>To</strong><strong> \: Find :</strong><strong>}</strong><strong>$

• Height of leader reach

$\bf </strong><strong>\</strong><strong>o</strong><strong>r</strong><strong>a</strong><strong>n</strong><strong>g</strong><strong>e</strong><strong>{</strong><strong>Solution</strong><strong> :</strong><strong>}</strong><strong>$

$\frac{p}{h} = \sin \theta \\ \\ \frac{9}{x} = \sin60 \degree \\ \\ \frac{9}{x} = \frac{ \sqrt{3} }{2} \\ \\ \sqrt{3}x = 18 \\ \\ x = \frac{18}{ \sqrt{3} } \\ \\ x = \frac{18}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ x = \frac{ \cancel{18 }\sqrt{3} }{ \cancel3} \\ \\ x = 6 \sqrt{3} \\ \\ x = 6 \times 1.7 \\ \\ \bf x = 7.8 \: m$

Ladder reach at a height of 7.8 m