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Math Help - Need help on these questions :(

  1. #1
    Rao
    Rao is offline
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    Need help on these questions :(

    Hi i need help on these question can some take out the time to explain them briefly

    Safety guidelines specify that a ladder should form an angle between 70° and 80° with the ground. If a ladder is 4 m long, determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines?

    A staircase is being constructed in a new house as displayed on the right. Each tread is 18 cm and each riser is 10 cm. Determine the angle of inclination of the stairs.


    A tunnel must be constructed through a mountain. The angle of elevation from one side of the mountain is 38.2°. The angle of elevation from the other side of the mountain is 27.4°. The height of the mountain is 575 m. What is the length of the tunnel through this mountain?

    Thanks in advance Please
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Rao View Post
    Hi i need help on these question can some take out the time to explain them briefly

    Safety guidelines specify that a ladder should form an angle between 70° and 80° with the ground. If a ladder is 4 m long, determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines?
    Hi

    The angle between the ground and the ladder is \theta where 70° \leq \theta \leq 80°

    The distance from the wall to the foot of the ladder is D = L\:\cos \theta where L is the length of the ladder
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  3. #3
    Senior Member Twig's Avatar
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    hi

    hi!

    Ladder:

    Distance from foot of ladder to wall is  4 \cdot cos(\theta) , where  \theta is the angle that may vary between 70 and 80 degrees.

    Denote the distance from the wall with x.
    Thus,  x_{min} = 4\cdot cos(80) \mbox{ and } x_{max} = 4 \cdot cos(70)


    For the mountain problem:

    If I interpreted the question right, (Im swedish lol) then:

    The angle the mountain walls make with the horizontal are  \alpha = 38.2 \mbox{ and } \beta = 27.4

    Denote the base of the mountain with d, then:
     d = 575(\frac{1}{tan(\alpha)} + \frac{1}{tan(\beta)})

    Here I drew a vertical line to the top of the mountain, and the length of this line is 575. Call this line h. By using the fact that  tan(\alpha) = \frac{h}{b} , where b is the base of a right triangle, the width of the mountain so to speak becomes a sum (see above).

    For the staircase, I didnīt get the question
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