Question

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?

Answer 1

A 20 foot ladder would need to be 15 degrees

Answer 2

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°