anna has a 10 foot long ladder that she is going to rest against a vertical wall along the bottom of a window still that is 8.5
feet above the ground. The safety code recommends that the angle the ladder makes with the ground be no greater than 65 degrees. Will the ladder be safe resting on the window still? Draw a diagram and show work to support your answer
1 answer:
As you can see in the picture, the ladder leaning against the wall makes a right triangle with the sides being the wall, the ground and the ladder. The ladder is opposite the right angle and so is the hypotenuse (the longest side of the triangle). The angle between the ladder and the ground is labeled a.
We know the height of the ladder (10 feet) and also the height off the ground of the windowsill (8.5 feet). That second side is opposite the angle a. So, when we consider angle a we know the length of the side opposite and of the hypotenuse.
Recall the sin of an angle can be found by using (opposite/hypotenuse).
So we have: sin a = 8.5 / 10. That is, sin a = .85
We are looking for the angle whose sin is .85 and can find this using the inverse sin function.
a is approximately 58.211669 degrees which is less than the 65 degrees and so safe.
Just to be on the safe side, I remind you that your calculator must be in degrees (not radians) to do this problem.
We know the height of the ladder (10 feet) and also the height off the ground of the windowsill (8.5 feet). That second side is opposite the angle a. So, when we consider angle a we know the length of the side opposite and of the hypotenuse.
Recall the sin of an angle can be found by using (opposite/hypotenuse).
So we have: sin a = 8.5 / 10. That is, sin a = .85
We are looking for the angle whose sin is .85 and can find this using the inverse sin function.
a is approximately 58.211669 degrees which is less than the 65 degrees and so safe.
Just to be on the safe side, I remind you that your calculator must be in degrees (not radians) to do this problem.
You might be interested in
Step-by-step explanation:
The question is wrong. The correct equation is :
We know that the equation gives the relation between temperature readings in Celsius and Fahrenheit.
Therefore, giving that we know the value in Fahrenheit ''F'' we can find the reading in Celsius ''C''. This define a function C(F) that depends of the variable ''F''.
So for the incise (a) we answer Yes, C is a function of F.
For (b) we need to find the mathematical domain of this function. Giving that we haven't got any mathematical restriction, the mathematical domain of the function are all real numbers.
Dom (C) = ( - ∞ , + ∞)
For (c) we know that the water in liquid state and at normal atmospheric pressure exists between 0 and 100 Celsius.
Therefore the range will be
Rang (C) = (0,100)
Now, we need to find the domain for this range. We do this by equaliting and finding the value for the variable ''F'' :
For C = 0 :
⇒
And for C = 100 :
⇒
Therefore, the domain as relating temperatures of water in its liquid state is
Dom (C) = (32,212)
For (d) we only need to replace in the equation by and find the value of C ⇒
⇒
≅ 21.67
C(71) = 21.67 °C
