A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall. What angle will a 35-ft. ladder make the horizontal if it reaches the sample spot?

So first you must find the height at which the "spot" is where the ladder touches the wall...

sin60=h/30

h=30sin60

Now we can find the angle that the 35 ft ladder make when it touches the same spot.

sinα=h/35 and using h we found earlier...

sinα=(30sin60)/35

α=arcsin[(30sin60)/35]

α≈47.93 (α≈47º55'42")

Answer Link

psm22415 psm22415 · Answer 2 · 2021-12-01T06:19:55+01:00

The angle will a 35-ft. ladder make the horizontal if it reaches the sample spot is [tex]sin^{-1}(47.93)[/tex].

Given that,

A 30-ft. ladder makes an angle of 60 degrees with the horizontal.

We have to find,

The angle will a 35ft. ladder make the horizontal if it reaches the sample spot.

According to the question,

A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall.

[tex]sin\theta = \frac{h}{30} \\sin60 = \frac{h}{30} \\[/tex]

h = 30sin60

Then, the angle will a 35-ft. ladder make the horizontal if it reaches the sample spot.

[tex]sin\alpha = \frac{30sin60}{35}\\sin\alpha = \frac{6 sin60}{7} \\\alpha = sin^{-1}(47.93)[/tex]

Hence, The angle will a 35-ft. ladder make the horizontal if it reaches the sample spot is [tex]sin^{-1}(47.93)[/tex]

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