how high is the sun in the sky?

[hongw]

Think of the ground you are standing on as the xy-plane. The vector (12,5,10) points from you toward the Sun. How high is the Sun in the sky? ????

 

[pappus]

Think of the ground you are standing on as the xy-plane. The vector (12,5,10) points from you toward the Sun. How high is the Sun in the sky? ????

1. Actually you are dealing with a cuboid (see attachment)

2. Use the dark grey right triangle to determine the length of the orange diagonal. (I've got 13)

3. Use the light grey right triangle to determine the value of the angle \(\displaystyle \alpha\). Use the tan-function. (I've got \(\displaystyle \alpha \approx 37.57°\) )

 

[hongw]

Thank you

So we are trying to find the length of the red line:

Cos(37.57)=Hypotenuse/Ajacent=redline/13

redline=cos(37.57)*13=10.30

so the answer is 10.30 ??

 

[pappus]

Thank you

So we are trying to find the length of the red line:

Cos(37.57)=Hypotenuse/Ajacent=redline/13

redline=cos(37.57)*13=10.30

so the answer is 10.30 ??

1. No

2. The "height" of a star (or the sun) is defined as the angle between the star and the horizont, measured in a plane perpendicular to the horizontal plane: The dark grey triangle is the in the horizontal plane and the light grey triangle is the before mentioned plane, perpendicular to the horizontal plane.

3. A sailor "shoots" the sun when he measured the angle between the sun and the horizont with a sextant. The answer I gave you (\(\displaystyle \alpha \approx 37.57°\)) is the final answer.

4. Sorry that I can't explain the situation more clearly but my English is obviously too limited to succeed.

 

[hongw]

I understand now, thank you so much again !