Question

suppose you identify a star with a declination of +38°. if you are located at a latitude of 82° north, what will the stars altitude h be, in degrees, when it crosses the meridian? h = degrees radians hints: 1% deduction per hint. hints remaining: 2 feedback: 1% deduction per feedback. 10 submission(s) remaining submit hint i give up! log100 atan() cotan() sin() exp() acotan() asin() cos() fact() in() acos() tan() √() + - 1 ( ) backspace 0 1 4 7 2 5 8 3 6 9 enter problem set #4 begin date: 9/25/2025 12:01:00 am due date: 10/2/2025 11:59:00 pm end date: 10/5/2025 11:59:00 pm

Explanation:

Step1: Recall the formula for star - altitude

The formula for the altitude \(h\) of a star when it crosses the meridian is \(h = 90^{\circ}-|\varphi-\delta|\), where \(\varphi\) is the observer's latitude and \(\delta\) is the star's declination.

Step2: Identify the values of \(\varphi\) and \(\delta\)

The observer's latitude \(\varphi = 82^{\circ}\) North and the star's declination \(\delta=38^{\circ}\).

Step3: Calculate the altitude

Since both \(\varphi\) and \(\delta\) are in the Northern hemisphere, we substitute into the formula: \(h = 90^{\circ}-|82^{\circ}- 38^{\circ}|\). First, calculate the value inside the absolute - value: \(82^{\circ}-38^{\circ}=44^{\circ}\). Then, \(h = 90^{\circ}-44^{\circ}=46^{\circ}\).

Answer:

46