raju wants to exrect the tent pole of height 10m with the support of four ropes each rope has to make an angle 45degress with the pole what should the length of the total rope
Answers
Answer:
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Step-by-step explanation:
Answer:
Step 1: Draw a figure from the given information.
GIVEN: Height of the pole AB = 10 m
Angle between the rope and pole \angle CAB\ =\ 30\degree∠CAB = 30°
Length of the rope AC = ?
Step 2: Determine the length of the rope by using the trigonometric ratios.
EXAMPLE: We need to find the rope length(hypotenuse)
So, take \cos A = \frac{adjacent}{hypotenuse}cosA=
hypotenuse
adjacent
\cos 30\degree = \frac{AB}{AC} = \frac{10}{AC} cos30°=
AC
AB
=
AC
10
\frac{\sqrt{3}}{2} = \frac{10}{AC}
2
3
=
AC
10
(Since \cos 30\degree = \frac{\sqrt{3}}{2}cos30°=
2
3
)
AC = \frac{2*10}{\sqrt{3}} AC=
3
2∗10
Simplify
AC = \frac{20}{\sqrt{3}} \frac{\sqrt{3}}{\sqrt{3}} AC=
3
20
3
3
( \because ∵ Rationalization)
AC = \frac{20\sqrt{3}}{3}AC=
3
20
3
AC = \frac{20 * 1.732}{3}AC=
3
20∗1.732
( \because ∵ \sqrt{3} = 1.732
3
=1.732 )
AC = 11.55 m
Length of the rope = 11.55 m
