Question

 A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be

7.5m

7.7m

8.5m

None of These

​

Answer 1

✬ Height = 7.5 m ✬

Step-by-step explanation:

Given:

• A ladder 15 m reaches the top of a vertical wall.
• Ladder makes an angle of 60° with the wall.

To Find:

• What is the height of wall ?

Solution: Let AC be a ladder of 15 m , BC be a vertical wall.

Now, In right angled ∆ABC we have

• BC = wall ( Perpendicular )
• BA = ground ( Base )
• AC = ladder ( Hypotenuse )
• ∠BCA = 60° ( Angle between ladder and wall )
• ∠CAB = 90° – 60° = 30° ( Angle between ladder and ground )

As we know that

★ sin θ = Perpendicular/Hypotenuse ★

From ∆ABC

$\implies{\rm }$ sin 30° = BC/AC

$\implies{\rm }$ 1/2 = BC/15

$\implies{\rm }$ 15 = 2BC

$\implies{\rm }$ 15/2 = BC

$\implies{\rm }$ 7.5 = BC

Hence, the height of wall is BC = 7.5 m.. Option A is correct.

Answer 2

$\sf\color{gray} Given:-$

AC = 15 m

∠A = 60°

∠C = 180°-(60°+90°) = 30°

$\sf \color {gray} To \: find:-$

AB or height of wall.

$\sf \color{gray}Solution:-$

$\boxed{\purple {\rm{sin30 \degree \: = \frac{AB}{AC} = \frac{ 1 }{2}}}}$

$\rm \frac{AB}{AC} = \frac{ 1 }{2}$

$\rm \frac{AB}{15} =\frac{ 1 }{2}$

$\rm AB = \frac{ 1 }{2} \times 15$

$\rm{AB = 7.5}$

$\rm {\underline{\underline{ \red{AB = 7.5\: m}}}}$