What is the Angle Formed by a Leaning Ladder Against a House?

[xyz_1965]

A 16 foot ladder is leaning against a house. It touches the bottom of a window that is 12, feet 6 inches above the ground. What is the measure of the angle that the ladder forms with the ground?

I will use sin (x), where x is the
measure of the angle that the ladder forms with the ground.

I think it best for me to convert 12 feet, 6 inches to inches. So, we have 50 inches.

sin (x) = 50/16

arcsin (sin x) = arcsin (50/16)

x = 0.0165919

Can the angle be left as a decimal answer? If not, how do I change 0.0165919 to degrees?

 

[MarkFL]

If you convert 12.5 ft. to inches (which is 150 in.) you must do the same to the other.

To convert to degrees recall there are \(\displaystyle \pi\) radians in 180 degrees.

 

[xyz_1965]

A 16 foot ladder is leaning against a house. It touches the bottom of a window that is 12, feet 6 inches above the ground. What is the measure of the angle that the ladder forms with the ground?

I will use sin (x), where x is the
measure of the angle that the ladder forms with the ground.

I think it best for me to convert 12 feet, 6 inches to inches. So, we have 50 inches.

sin (x) = 50/16

arcsin (sin x) = arcsin (50/16)

x = 0.0165919

Can the angle be left as a decimal answer? If not, how do I change 0.0165919 to degrees?

Given 0.0165919, I know it really means. 0° 0' 0.0165919".

I can use D + m/60 + s/3600, where D represents degrees, m is minutes and s is seconds.

= 0° + 0'/60 + 0.0165919"/3600
= 0.000004608861 degrees.

Is this right, Mark?

 

[MarkFL]

Given 0.0165919, I know it really means. 0° 0' 0.0165919".

I can use D + m/60 + s/3600, where D represents degrees, m is minutes and s is seconds.

= 0° + 0'/60 + 0.0165919"/3600
= 0.000004608861 degrees.

Is this right, Mark?

No, presumably the angle you have is in radians which is not the same as arc-seconds.

 

[xyz_1965]

No, presumably the angle you have is in radians which is not the same as arc-seconds.

Can show me how to make the conversion?

 

[MarkFL]

Can show me how to make the conversion?

Use this:

To convert to degrees recall there are \(\displaystyle \pi\) radians in 180 degrees.

 

[xyz_1965]

Use this:

What do you mean? Multiply the given decimal number by π? Are you saying to multiply the given decimal number by 180 degrees? Are you saying to use π/180°?

 

[MarkFL]

What do you mean? Multiply the given decimal number by π? Are you saying to multiply the given decimal number by 180 degrees? Are you saying to use π/180°?

Like with any unit conversion, you want to multiply by 1 in the form of a fraction containing some number of the desired unit over the equivalent number of current units. In this case, it would be:

\(\displaystyle \frac{180^{\circ}}{\pi}\)

 

[xyz_1965]

Like with any unit conversion, you want to multiply by 1 in the form of a fraction containing some number of the desired unit over the equivalent number of current units. In this case, it would be:

\(\displaystyle \frac{180^{\circ}}{\pi}\)

Are you saying to multiply the given decimal number by \(\displaystyle \frac{180^{\circ}}{\pi}\)?

 

[MarkFL]

Are you saying to multiply the given decimal number by \(\displaystyle \frac{180^{\circ}}{\pi}\)?

Yes, that will convert an angle in radians to the same angle in degrees.

 

[xyz_1965]

Yes, that will convert an angle in radians to the same angle in degrees.

Good to know.