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 $$\pi$$ 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 $$\pi$$ 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:

$$\frac{180^{\circ}}{\pi}$$

 

[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:

$$\frac{180^{\circ}}{\pi}$$

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

 

[MarkFL]

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

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.