Mathematics

Question

A 10-foot ramp must make an angle of 30° with the ground if it is to reach a certain window. What angle must a 15-foot ramp make with the ground to reach the same window?

2 Answer

  • In solving problems like this, it's best to work on a diagram (see attached image). First, given the angle formed by the ramp and the length of the ramp, we can apply the properties of right triangles and recall that 

    [tex] sin \theta = \frac{opposite}{hypotenuse} [/tex]

    Hence, we have

    [tex] \sin 30^{0} = \frac{h}{10} [/tex]
    [tex] \frac{1}{2} = \frac{h}{10} [/tex]
    [tex] h = 5 [/tex]

    Now that we have the window's height, we can compute for the angle, θ, if the ramp has a length of 15.

    [tex] \sin \theta = \frac{5}{15} [/tex]
    [tex] \theta = \sin^{-1}(\frac{1}{3}) [/tex]
    [tex] \theta = 19.47 [/tex]

    Therefore, for the 15-foot ramp to reach the window, the ramp must form an angle of 19.47°.

    Answer: 19.47°
  • Answer:

    19.5

    Step-by-step explanation:

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