Answer:
The ladder reaches (4)(√3) ft up the wall (6.93 ft)
Step-by-step explanation:
Think of a triangle with a 60 degree angle in the lower left corner. The lower right corner is a right triangle, and 8 ft is the length of the hypotenuse. The other angle is 30 degrees.
We know the angle 60 degrees, plus the length of the hypotenuse, but need the length of the vertical side opposite the 60 degree angle. Use the sine function here because it involves these knowns:
opposite side
sin 60 degrees = ------------------------ = x/(8 ft) = (√3)/2
Cross-multiplying, we get:
2x = (8 ft)(√3), or through reduction, x = (4)(√3)
The ladder reaches (4)(√3) ft up the wall (6.93 ft)
With the ground, [tex]6.92 ft[/tex] the wall does the ladder reach.
A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle.
According to the question
An eight foot ladder leans against a building. if the ladder makes an angle of 60° with the ground.
From the right angle triangle,
[tex]sin 60^{0} =\frac{h}{8}[/tex]
[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{h}{8}[/tex]
[tex]8\sqrt{3} =2h[/tex]
[tex]h = 4\sqrt{3}[/tex]
[tex]h = 6.92 ft[/tex]
Hence, With the ground, [tex]6.92 ft[/tex] the wall does the ladder reach.
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