A ladder is leaned against a vertical wall makes an angle of 20 degee with the ground. The foot of the ladder is 3m from the wall. Find the length of the ladder
Answers
Answer:
Answer:
\green{\therefore{\text{Length\:of\:ladder=6\:m}}}∴Lengthofladder=6m
\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}
Step−by−stepexplanation:
• In the given question information given about a ladder leaning against a vertical wall makes an angle of 60 with the ground. the foot of the ladder is at distance of 3m from the wall.
• We have to find the Length of ladder.
\begin{gathered} \green{\underline \bold{Given :}} \\ : \implies \text{Distance\:between\:wall\:and\:foot\:of\:ladder=3\:m} \\ \\ : \implies \text{Angle\:of\:elevation}=60^{\circ}\\\\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Length\:of\:ladder= ?}\end{gathered}
Given:
:⟹Distancebetweenwallandfootofladder=3m
:⟹Angleofelevation=60
∘
ToFind:
:⟹Lengthofladder= ?
• Accroding to given question :
\begin{gathered} \bold{In \: \triangle \: ABC} \\ : \implies cos \: \theta = \frac{\text{Base}}{\text{Hypotenuse}} \\ \\ : \implies cos \: 60^{ \circ} = \frac{AB}{AC} \\ \\ : \implies \frac{1}{2} = \frac{3}{AC} \\ \\ : \implies AC = 3\times2 \\ \\ \green{ : \implies AC = 6 \: m} \\ \\ \green{\therefore \text{Length\: of \: ladder= 6 \: m}}\end{gathered}
In△ABC
:⟹cosθ=
Hypotenuse
Base
:⟹cos60
∘
=
AC
AB
:⟹
2
1
=
AC
3
:⟹AC=3×2
:⟹AC=6m
∴Lengthof ladder= 6 m
Step-by-step explanation:
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