from a window 35 meters high, the angle of depression to the top of a nearby street light is 55 degrees. The angle of depression to the base of the streetlight is 57.8. How tall is the streetlight?
look at my solution to #2 question (I erroneously called it #1)
the question is identical in structure to yours.
See if you can follow it, then do yours.
who is number 2?
yeah who is number 2
To find the height of the streetlight, we can use trigonometry and the concept of angle of depression. Here's how we can approach the problem:
Step 1: Draw a diagram:
Draw a diagram with a vertical line representing the window, another vertical line representing the streetlight, and a horizontal line representing the ground.
Step 2: Label the given information:
Assign variables to the unknowns in the problem. Let the height of the streetlight be 'h'.
Step 3: Identify the angles:
From the given information, we know the angle of depression to the top of the streetlight is 55 degrees and the angle of depression to the base of the streetlight is 57.8 degrees. Label these angles on the diagram.
Step 4: Identify the right-angle triangle:
From the diagram, we can see that we have a right-angle triangle formed by the window, the streetlight, and the ground.
Step 5: Use trigonometry:
Since we have a right-angle triangle, we can use trigonometric ratios to relate the angles and sides of the triangle. The tangent ratio is defined as opposite/adjacent.
In this case, we can use the tangent of the angle of depression to find the height of the streetlight (opposite side) and the distance from the window to the streetlight (adjacent side).
Step 6: Calculate the height of the streetlight:
Using the tangent ratio, we can set up the equation as follows:
tan(55 degrees) = h/distance from window to streetlight
Simplifying the equation, we have:
h = tan(55 degrees) * distance from window to streetlight
Step 7: Calculate the distance from the window to the streetlight:
To find the distance from the window to the streetlight, we can use another trigonometric ratio. In this case, we can use the tangent of the angle of depression to the base of the streetlight.
tan(57.8 degrees) = h + 35/distance from window to streetlight
Step 8: Solve for the height of the streetlight:
Using the second equation above, we can substitute the value of the distance from the window to the streetlight into the equation and solve for 'h'.
h = (tan(55 degrees) * distance from window to streetlight) - 35
Plug in the values and perform the calculations to find the height of the streetlight.
By following these steps, you should be able to calculate the height of the streetlight using the given angles and the height of the window.