A 50-foot ladder leans against a wall 15 feet from the base of the wall. What is the measure of the angle formed by the ladder a
nd the wall? Please show all work.
2 answers:
Answer:
72.5°
Step-by-step explanation:
This is a right triangle problem. The ladder is the hypotenuse, and we have a length for that of 50 feet. We also have the distance along the ground that the ladder's base is from the wall against which it is leaning. This is the side adjacent to the angle for which we are seeking, so it the side adjacent to the angle, and it measures 15 feet.
We need a trig ratio that relates the side adjacent to the hypotenuse. That will be the cosine. Setting up:
and then filling in:
Use the 2nd button on your calculator, and then press cos and you will get a display on your screen that looks like this:
After that open parenthesis enter the fraction 15/50 and hit enter and you'll get the angle of 72.5 degrees, rounded.
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Answer:
Step-by-step explanation:
In essence, one needs to work their way backwards to solve this problem. Use the information to construct the function.
The function has verticle asymptotes at (x = 4) and (x = 5). This means that the denominator must have (x - 4) and (x - 5) in it. This is because a verticle asymptote indicates that the function cannot have a value at these points, the function jumps at these points. This is because the denominator of a fraction cannot be (0), the values (x - 4) and (x - 5) ensure this. Since if (x) equals (4) or (5) in this situation, the denominator would be (0) because of the zero product property (this states that any number times zero equals zero). So far we have assembled the function as the following:
The function has x-intercepts at (6, 0), and (0, 10). This means that the numerator must equal (0) when (x) is (6) or (10). Using similar logic that was applied to find the denominator, one can conclude that the numerator must be (). Now one has this much of the function assembled
Finally one has to include the y-intercept of (0, 120). Currently, the y-intercept is (60). This is found by multiplying the constants together. (6 * 10) equals (60). One has to multiply this by (2) to get (120). Therefore, one must multiply the numerator by (2) in order to make the y-intercept (120). Thus the final function is the following: