The angle of elevation of the top of a flagpost from a point on a horizontal ground is found to be 30 degree. On walking 6m towards the post, the elevation increased by 15 degree. Find the height of the flagpost.
To find the height of the flagpost, we can use basic trigonometry.
Let's break down the problem step by step:
Step 1: Draw a diagram
Draw a diagram representing the situation. Draw a horizontal ground, a flagpost, a point (let's call it point A) on the ground where the angle of elevation is measured, and another point (let's call it point B) 6 meters towards the flagpost from point A, where the angle of elevation increases.
Step 2: Identify known values
From the problem, we know that the angle of elevation from point A is 30 degrees and when we walk 6 meters towards the flagpost to point B, the angle of elevation increases to 45 degrees.
Step 3: Identify what we need to find
We need to find the height of the flagpost. Let's call it h.
Step 4: Determine the relevant side lengths in the triangle
In triangle ABC (where A is the top of the flagpost, B is the first position, and C is where the angle of elevation is measured), we have two sides of interest: AB and BC. We know the length of AB is 6 meters.
Step 5: Use trigonometry
We can use the tangent function to find the height of the flagpost.
In triangle ABC, the tangent of the angle of elevation is equal to the opposite side (h) divided by the adjacent side (AB). So we have:
tan(30 degrees) = h / 6
Similarly, in triangle ABD (where A is the top of the flagpost, B is the second position, and D is where the angle of elevation is measured), we can use the tangent function again:
tan(45 degrees) = h / 0 (since BD is the adjacent side)
Step 6: Solve the equations
Using a calculator to find the tan(30 degrees) and tan(45 degrees), we can set up the equations:
tan(30 degrees) = h / 6
tan(45 degrees) = h / 0
Since the tangent of 45 degrees is 1:
1 = h / 0
The second equation tells us that h could be any value since we have 0 in the denominator. This is not useful for solving the problem.
So, we only have one equation left:
tan(30 degrees) = h / 6
Since tan(30 degrees) is equal to √3 / 3, we can rewrite the equation as:
√3 / 3 = h / 6
Step 7: Solve for h
To solve for h, we can cross-multiply and then divide:
6 * √3 = 3 * h
√3 * 2 = h
So, the height of the flagpost, h, is equal to √3 * 2 or approximately 3.46 meters.