Answer:
a) 31.058 m
b) 8.04 m
Step-by-step explanation:
Given that:
The angle between the ladder and the ground = 75°
Length of the wall = 30 m
Since the wall is perpendicular to the ground, the angle between the wall and the ground = 90°
a) Using sine rule which states that If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle,
[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)} =\frac{c}{sin(C)}[/tex]
Let us assume the Length of the wall = a = 30 m
The opposite angle = A = The angle between the ladder and the ground = 75°
c = Length of the ladder to reach top of the wall
The opposite angle = C =the angle between the wall and the ground = 90°
Therefore:
[tex]\frac{a}{sin(A)} =\frac{c}{sin(C)} \\c=\frac{a*sin(C)}{sin(A)} \\c=\frac{30*sin(90^0)}{sin(75^0)} =31.058m[/tex]
The length of the ladder is 31.058 m
b) Using Pythagoras theorem:
The length of the ladder = c, Length of the wall = a, Distance from wall to base of ladder = b
c² = a² + b²
31.058² = 30² + b²
964.6 = 900 + b²
b² = 964.6 - 900 = 64.6
b = √64.6 = 8.04
b = 8.04 m
The distance from the wall to the base of the ladder should be 8.04 m for safe climbing?
