A 10-foot ladder must make an angle of 30° with the ground if it is to reach a certain window. What angle must a 20-foot ladder
make with the ground to reach the same window?
2 answers:
Answer:
15°
Explanation:
Let the height of the window be 'h'
Let the angle the second ladder make with the ground be 'Ф'
From the image uploaded, height of the window 'h' will be calculated from figure a
Using SohCahToa; we calculate the height of the window 'h' that 10-foot ladder must reach.
sine30 = opposite/hypotenuse
sine 30 = h/10ft
h = 10ft × sine30
h = 10ft × 0.5
h= 5ft; height of the window is 5 foot
using figure b and substituting the value of h as 5ft, will calculate 'Ф' for 20-foot ladder
sine Ф = 5ft/20ft
sine Ф = 1/4
sine Ф = 0.25
Ф = arc sine (0.25)
Ф = 14.4775°
Ф ≅ 15°
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