The angle of elevation must be 68.202 degrees
Solution:
Given that, 14 foot ladder is used to scale a 13 foot wall
We have to find the angle of elevation must the ladder be situated in order to reach the top of the wall
The figure for this solution is attached below
The ladder, wall and the ground forms a right angled triangle
ABC is a right angled triangle
AB is the height of wall = 13 feet
AC is the length of ladder = 14 feet
We have to find the angle of elevation
Let the angle of elevation be "x"
For right angled triangle ABC, We can use the definition for sine
[tex]\sin x=\frac{\text { opposite }}{\text { hypotenuse }}[/tex]
Here, in figure, opposite = AB and hypotenuse = AC
[tex]\sin x=\frac{A B}{A C}\\\\\sin x = \frac{13}{14}\\\\\sin x = 0.9285\\\\x = sin^{-1}(0.9285)\\\\x = 68.202[/tex]
Thus the angle of elevation must be 68.202 degrees
The angle of elevation the ladder will be situated in order to reach the top of the wall is 68°.
A right triangle has one of its angles as 90 degrees. The angle of elevation can be found using trigonometric ratios.
Therefore, the angle of elevation can be calculated as follows;
The length of the ladder is the hypotenuse.
The opposite side is the height of the wall.
Therefore,
sin ∅ = opposite / hypotenuse
sin ∅ = 13 / 14
∅ = sin⁻¹ 0.92857142857
∅ = 68.2129901712
∅ = 68°
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