A flay pole is placed at the top of a tower.the angle of elevation of the bottom and top of the flay pole from a point on the ground 10M away and 40 degrees and 50degrees respectively.find the length of the flay pole.

let height of tower be h m

let height of "flay" pole be f m

two right-angled triangles:

tan40 = h/10
h = 10tan40

tan 50 = (h+f)/10
h+ f = 10tan50

continue

Thanks 🤗

To find the length of the flagpole, we can use trigonometric ratios. Let's first understand the given information.

From a point on the ground 10 meters away from the tower, the angle of elevation of the bottom of the flagpole is 40 degrees, and the angle of elevation of the top of the flagpole is 50 degrees.

We'll use the concept of trigonometry and specifically the tangent function to solve this problem. The tangent of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Here's how we can calculate the length of the flagpole step by step:

Step 1: Let's consider the triangle formed by the ground, the top of the flagpole, and the point where we're standing. In this triangle, the side opposite to the angle of 50 degrees is the length of the flagpole (let's call it 'x'). The side adjacent to this angle is the distance from the point on the ground to the bottom of the flagpole, which is 10 meters.

Step 2: We can use the tangent function for the angle of 50 degrees to set up an equation:

tan(50) = x/10

Step 3: Now, let's calculate the value of 'x' by solving this equation:

x = 10 * tan(50)

Using a calculator, we find that x ≈ 13.28 meters.

Hence, the length of the flagpole is approximately 13.28 meters.