Question

A ladder 14 meter long rests a againsts a wall if the foot of the ladder is 7m from the wall then the angel of elevation of the ladder is

Answer 1

✬ Angle = 60° ✬

Step-by-step explanation:

Given:

• Length of ladder is 14 meter.
• Foot of ladder is at 7 m from foot of wall.

To Find:

• Angle of elevation ?

Solution: Let angle of elevation be θ , AC be the window , BC be the ladder and AB be the distance between foot of ladder and window.

In ∆ABC we have

• BC {hypotenuse} = 14

• AB {base} = 7

• AC {perpendicular}

• ∠ABC = θ

As we know that

★ Cosθ = Base/Hypotenuse ★

➮ cos θ = AB/BC

➮ cos θ = 7/14

➮ cos θ = 1/2

➮ cos θ = 60°

• { cos 60° = 1/2 or 1/2 = cos θ or 60° }

Hence, angle of elevation of the ladder is 60°.

Answer 2

Diagram :

$\setlength{\unitlength}{20mm}\begin{picture}(6,2)\linethickness{0.4mm}\put(7.7,2.9){\large\sf{A}}\put(7.9,0.8){\large\sf{B}}\put(10.4,0.8){\large\sf{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(7.5,1.9){\sf{\large{ 7 m}}}\put(9,0.7){\sf{\large{ ? }}}\put(9.8,2.2){\sf{\large{14m}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\multiput(8.1,2.8)(.33,-.25){8}{\line(2,1){.3}}\qbezier(11,1)(10.5,1.4)(8.35,3)\end{picture}$

$</p><p>\green{\underline \bold{Given :}} \\ : \implies \text{Length\:of\: ladder= 14\: m} \\ \\ : \implies \text{Height\:of\:wall=7\:m}\\\\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Angle\:of\:elevation= ?}$

• Accroding to given question :

$\bold{in \: \triangle \: ABC} \\ : \implies \sf \: cos \: \theta = \frac{\text{Base}}{\text{Hypotenuse}} \\ \\ : \implies \sf \: cos\: \theta= \frac{BC}{AC} \\ \\ : \implies \sf \: cos\:\theta= \frac{7}{14} \\ \\ : \implies \sf \: cos\:\theta= \frac{1 }{2} \\ \\ \green{ : \sf \: \implies \theta = 60^{\circ} }$