Two telescopes A and B spot a star. Telescope A reports the position of the star to be in the East 60 degrees above the horizontal line joining A and B. Telescope B, which is 500 km West of telescope A spots the star at 30 degrees above the horizontal line joining A and B. What is the star's altitude above the adjoining horizontal line?
To calculate the star's altitude above the adjoining horizontal line, we need to find the angle between the line connecting the two telescopes (A and B) and the horizontal line.
Let's break down the problem step by step:
Step 1: Draw a diagram
Draw a diagram of the situation, indicating the positions of telescopes A and B, and the star. The horizontal line represents the line joining A and B, and the star's altitude will be measured with respect to this line.
Step 2: Determine the angles
From the information given, we know that telescope A spots the star in the East 60 degrees above the horizontal line. This means that the angle between the horizontal line and the line connecting A and the star is 60 degrees.
Similarly, telescope B spots the star at 30 degrees above the horizontal line. This means that the angle between the horizontal line and the line connecting B and the star is 30 degrees.
Step 3: Calculate the star's altitude
To find the star's altitude above the adjoining horizontal line, we need to calculate the angle between the lines connecting A and B, and the horizontal line.
Since telescope B is 500 km West of telescope A, we can conclude that the angle between the telescope lines is 180 degrees (since West is opposite to East on a compass).
To find the star's altitude, we'll subtract the angles between the telescope lines and the horizontal line:
Star's altitude = (180 degrees - 60 degrees - 30 degrees) = 90 degrees
Therefore, the star's altitude above the adjoining horizontal line is 90 degrees.