Answer:
A) The length of Ladder is 28.7 feet.
B)The length of the wall up to where the ladder reaches is 28.5 feet.
Step-by-step explanation:
Consider a wall AB and a ladder AC .
The ladder is leaning against a wall and make an 82 degree angle of elevation with the ground that is ∠ACB = 82°
Part A) If the base of the ladder is 4 feet from the wall that is BC= 4 feet.
We have to find the length of ladder (AC).
Consider Δ ABC , with ∠B= 90°
Applying trigonometric ratio,
[tex]\cos C=\frac{\text{Base}}{\text{Hypotenuse}}[/tex]
Substitute the values, we get,
[tex]\cos C=\frac{BC}{AC}[/tex]
[tex]\Rightarrow \cos 82^{\circ}=\frac{4}{AC}[/tex]
Solve for AC, we get,
[tex]\Rightarrow AC=\frac{4}{\cos 82^{\circ}}[/tex]
[tex]\Rightarrow AC=28.7[/tex] (approx)
Thus, the length of Ladder is 28.7 feet.
B) To determine the length of the wall up to where the ladder reaches,
Applying trigonometric ratio,
[tex]\tan C=\frac{\text{Perpendicular}}{\text{Base}}[/tex]
Substitute the values, we get,
[tex]\tan C=\frac{AB}{BC}[/tex]
[tex]\Rightarrow \tan 82^{\circ}=\frac{AB}{4}[/tex]
Solve for AB, we get,
[tex]\Rightarrow AB=\tan 82^{\circ} \times 4[/tex]
[tex]\Rightarrow AC= 28.5[/tex] (approx)
Thus, the length of the wall up to where the ladder reaches is 28.5 feet.
