This is another application that I didn't understand
A blimp, suspended in the air at a height of 500 ft, lies directly over a line from Soldier Field to the Planetarium on Lake Michigan. If the angle of depression from the blimp to the stadium is 32 degrees and from the blimp to the planetarium is 23 degrees, fin the distance between soldier Field and the Planetarium.
1978.09
To find the distance between Soldier Field and the Planetarium, we can use trigonometry and the concept of angles of depression.
Let's label the distance between Soldier Field and the blimp as "x" and the distance between the Planetarium and the blimp as "y". We are trying to find the value of "x + y".
Given that the blimp is suspended at a height of 500 ft, we can consider a right-angled triangle formed between the blimp, the stadium, and the ground. The angle of depression from the blimp to the stadium is 32 degrees. Since this angle is between the hypotenuse (the line from the blimp to the stadium) and the horizontal ground, we can use the tangent function to find the value of "x".
Using the tangent function, we have:
tan(32 degrees) = x / 500 ft
Simplifying the equation, we get:
x = 500 ft * tan(32 degrees)
Similarly, we can consider another right-angled triangle formed between the blimp, the planetarium, and the ground. The angle of depression from the blimp to the planetarium is 23 degrees. Again, using the tangent function, we can find the value of "y":
tan(23 degrees) = y / 500 ft
Simplifying the equation, we have:
y = 500 ft * tan(23 degrees)
Now, we can find the value of "x + y" by substituting the calculated values of "x" and "y" in the above equations and adding them:
x + y = (500 ft * tan(32 degrees)) + (500 ft * tan(23 degrees))
Calculating this expression will give us the distance between Soldier Field and the Planetarium.