Given:
• Height of ladder = 7 m
,
• DIstance of foot of ladder to the wall = 4.5 m
Let's find the angle of elevation of the ladder.
First sketch the figure representing this situation.
Where x is the angle of elevation of the ladder.
Let's solve for x.
To solve for x, apply the Trigonometric ratio formula for cosine.
[tex]\cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
Where:
• Adjacent side is the side adjacent to the angle x = 4.5
,
• Hypotenuse is the longest side = 7
,
• θ is the angle = x
Hence, we have:
[tex]\cos x=\frac{4.5}{7}[/tex]
Take the cos inverse of both sides:
[tex]\begin{gathered} x=\cos ^{-1}(\frac{4.5}{7}) \\ \\ x=49.9\approx50^o \end{gathered}[/tex]
Therefore, the angle of elevation of the ladder is 50 degrees.
ANSWER:
c. 50 degrees
