A pole 10 m high was observed from the point B where its shadow was equal to the pole Find the length of its shadow from another point on the same line where the angle of elevation of the top of the pole is 2/3 of the previous angle of elevation. ​ step by step

Sure, let's solve this step by step.

Step 1: Understand the problem The problem states that there is a pole of 10m height. From point B, the shadow of the pole is equal to the height of the pole. This means that the angle of elevation from point B is 45 degrees (since in a 45-45-90 triangle, the two legs are equal). We need to find the length of the shadow from another point where the angle of elevation is 2/3 of the previous angle of elevation.

Step 2: Calculate the new angle of elevation The new angle of elevation is 2/3 of 45 degrees, which is 30 degrees.

Step 3: Use the tangent of the angle to find the length of the shadow In a right triangle, the tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the pole (10m) and the adjacent side is the length of the shadow we want to find. So, we have:

tan(30) = 10 / shadow_length

Step 4: Solve for shadow_length Rearranging the equation from step 3, we get:

shadow_length = 10 / tan(30)

Step 5: Calculate the value The tangent of 30 degrees is approximately 0.577, so:

shadow_length = 10 / 0.577 = approximately 17.32m

So, the length of the shadow from the other point is approximately 17.32m.