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In effect you have the outline of aright-angled triangle with an adjacent side of 10 ft and an opposite side of 15 ft and you need to find the length of the hypotenuse (which will be the ladder). Use Pythagoras' theorem to find the length of the hypotenuse: adjacent2+opposite2 = hypotenuse2 102+152= 325 square feet The square root of 325 = 18.02775638 feet So the ladder needs to be at least 18 feet in length.
Using Pythagoras' theorem the length of the ladder is 20.248 feet
step ladder
Yes because tangent = opposite/adjacent
Extension Ladder
12
Providing that the ground is level and that the wall is straight, you have the outline of a right angled triangle with an adjacent angle of 73 degrees and an adjacent length of 1.17 metres. In order to find the length of the hypotenuse (which is the ladder itself) we use the cosine ratio: cosine = adjacent/hypotenuse Which when rearranged is: hypotenuse = adjacent/cosine hypotenuse = 1.17/cosine73 degrees = 4.001755235 So the length of the ladder is 4 metres correct to one significant figure.
You divide the length of one adjacent side by the length of the other adjacent side.
Assuming it is a two section ladder then it must therefore have a minimum length of 28 feet.
In effect you have the outline of aright-angled triangle with an adjacent side of 10 ft and an opposite side of 15 ft and you need to find the length of the hypotenuse (which will be the ladder). Use Pythagoras' theorem to find the length of the hypotenuse: adjacent2+opposite2 = hypotenuse2 102+152= 325 square feet The square root of 325 = 18.02775638 feet So the ladder needs to be at least 18 feet in length.
Using Pythagoras' theorem the length of the ladder is 20.248 feet
From the US OSHA Construction standards:1926.1053(b)(1)When portable ladders are used for access to an upper landing surface, the ladder side rails shall extend at least 3 feet (.9 m) above the upper landing surface to which the ladder is used to gain access; or, when such an extension is not possible because of the ladder's length, then the ladder shall be secured at its top to a rigid support that will not deflect, and a grasping device, such as a grabrail, shall be provided to assist employees in mounting and dismounting the ladder. In no case shall the extension be such that ladder deflection under a load would, by itself, cause the ladder to slip off its support.
Its Tangent, APEX "The tangent of an angle is the ratio of the opposite leg length to the adjacent leg length."
This answer uses trigonometry to avoid a lot of work:tangent = opposite/adjacent and tangent*adjacent (base of ladder from the building) = opposite (height of ladder above ground)So: tangent 60 degrees*3 = 5.196152423Therefore: Top of the ladder above ground = 5.2 meters correct to one decimal place.More laborious methodThe right triangle formed by the wall, ground and ladder has sides in the ratio of 1::2::sq-rt-of-3. The shortest side is the one opposite the 30 degree angle, i.e., the given distance from wall to base of the ladder--3 m.The length of the ladder represents the hypotenuse of the triangle, and is twice as long, hence 6 m.And the height of the ladder's top from the ground is proportional to the third side whose length is sq-rt-3 times that of the shortest side. Sq-rt-3 is about 1.732, so height of the ladder's top at the wall is about 5.20 m, or 520 cm.
step ladder
Yes because tangent = opposite/adjacent
Extension Ladder