The feet of two vertical poles of heights 3m and 7m are in line with a point P on the ground the smaller pole being between the taller pole and at a distance 20m from P.The angle of elevation of the top . T of the taller pole from the top R of the smaller pole is 30°.(i) calculate distance RT (ii) distance of the foot of the taller pole from P.

height difference is 4m

4m / RT = sin(30º)

RT=0.125 is Wrong

RT = 8 is the answer

angle of elevation and depression

To solve this problem, we can use the concept of similar triangles. Let's break it down step by step.

(i) To calculate the distance RT:

Step 1: Draw a diagram.
Draw two vertical poles labeled A and B. Let A be the taller pole, and B be the smaller pole. Label the height of A as 7m and the height of B as 3m.
Label the point where the feet of the poles meet as P, and label the top of pole A as T and the top of pole B as R. Finally, label the distance between P and B as 20m.

Step 2: Identify the triangles.
We have two triangles in this problem: triangle PRT and triangle PBA.

Step 3: Identify the similar triangles.
Triangle PRT is similar to triangle PBA. The corresponding angles are angle P and angle P, and angle R is congruent to angle A.

Step 4: Set up a proportion.
Since the triangles are similar, we can set up the following proportion:

PR / PA = RT / BA

Step 5: Substitute the values.
Plug in the known values into the proportion.
We know that PR = 20m (given), and PA = 3m (height of smaller pole).

20 / 3 = RT / 7

Step 6: Solve for RT.
Cross-multiply and solve for RT:

(20 * 7) / 3 = RT

RT ≈ 46.67m

Therefore, the distance RT is approximately 46.67m.

(ii) To calculate the distance of the foot of the taller pole from P:

Step 1: Draw a diagram (same as above).

Step 2: Identify the triangles.
We have two triangles in this problem: triangle PTR and triangle PAB.

Step 3: Identify the similar triangles.
Triangle PTR is similar to triangle PAB. The corresponding angles are angle P, angle T, and angle R, which are congruent to angles P, A, and B, respectively.

Step 4: Set up a proportion.
Since the triangles are similar, we can set up the following proportion:

PT / PA = TR / AB

Step 5: Substitute the values.
Plug in the known values into the proportion.
We know that PT = 3m (height of smaller pole), and PA = 3m (height of smaller pole).

3 / 3 = TR / 20

Step 6: Solve for TR.
Cross-multiply and solve for TR:

(3 * 20) / 3 = TR

TR = 20m

Therefore, the distance of the foot of the taller pole from P is 20m.

RT = 0.125