how do I set up this problem a man standing on the deck of a ship with his eyes 25 feet above sea level notes that the angle of elevation to the top of a 25 foot lighthouse is 3 degrees 27 minutes. how far is the boat from the lighthouse
Did you not read our objection to your problem.
Why would you repost exactly the same way ?
http://www.jiskha.com/display.cgi?id=1393701722
Steve gave you a solution according to one interpretation.
To set up this problem, we can use the concepts of trigonometry. We can form a right triangle with the man's eyes, the top of the lighthouse, and the distance between the boat and the lighthouse. Here's how you can set up this problem step by step:
Step 1: Draw a diagram
Draw a right triangle to represent the situation described. Label the parts of the triangle as follows:
- The bottom edge represents the distance between the boat and the lighthouse (let's call it 'd').
- The vertical side represents the height of the lighthouse, which is 25 feet.
- The top angle of the triangle represents the angle of elevation, which is given as 3 degrees 27 minutes.
Step 2: Identify the known and unknown variables
In this problem, the known variables are:
- The height of the lighthouse: 25 feet
- The angle of elevation: 3 degrees 27 minutes
The unknown variable is the distance between the boat and the lighthouse, which we need to calculate.
Step 3: Convert the angle from degrees and minutes to degrees
Since trigonometric functions typically work with angles in degrees, we need to convert the given angle from degrees and minutes to decimal degrees. To do this, we divide the minutes by 60 and add the result to the degrees.
3 degrees + (27 minutes / 60) = 3.45 degrees (rounded to two decimal places)
Step 4: Apply trigonometric function
In this case, we can use the tangent function because we have the opposite and adjacent sides of the right triangle. The tan of an angle is equal to the ratio of the opposite side to the adjacent side.
tan(3.45 degrees) = 25 feet / d
Step 5: Solve for d
To find the value of 'd', rearrange the equation:
d = 25 feet / tan(3.45 degrees)
Now, you can use a calculator to evaluate the tan(3.45 degrees) and then divide 25 feet by that value to find the distance 'd.'
Note: Make sure your calculator is set to degrees mode when calculating trigonometric functions.