First, draw a picture of the situation.
Let the length of the ladder be X.
Notice that X is the hypotenuse of a right triangle.
Notice that the side opposite of the known angle is known.
Remember that the sine of an angle is (side opposite)/(hypotenuse), so that sin46o=15'/X
solving for X gives X=20.85'
112
It can be any angle that is more than zero degrees and less than 90 degrees. <><><> It will be an ACUTE angle, and if the ladder is placed properly (1 ft out for each 4 ft up) the angle between wall and ladder will be ABOUT 18 degrees.
18
15*cos(60) = 7.5 7.5 m
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.
112
It can be any angle that is more than zero degrees and less than 90 degrees. <><><> It will be an ACUTE angle, and if the ladder is placed properly (1 ft out for each 4 ft up) the angle between wall and ladder will be ABOUT 18 degrees.
18
First, you would need a ladder approximately 93 million miles long and able to withstand the massive temperatures the sun creates (the corona is around 1 million degrees, the surface is around 5,000 degrees, and the core is around 15 million degrees Fahrenheit). Even if you had this ladder, the sun has no solid surface against which to prop the ladder, and the Earth's rotation would prevent you from having the legs of the ladder on the ground while still pointing the top of the ladder at the sun. In short, the answer is "No".
15*cos(60) = 7.5 7.5 m
115
32
Round the base angle to 70 degrees and use the sine ratio: 30*sine 70 degrees = 28.19077862 feet Height of ladder from the ground = 28 feet to 2 s.f.
170 newtons
The ladder forms a right angle with the building: the ground and the building forming the right angle and the ladder forming the hypotenuse. If the length of the ladder is L metres, then sin(49) = 12/L So L = 12/sin(49) = 15.9 = 16 metres.
18
8