Question

Mr. Selcom wanted to know the height of the tree. What he did was form a point A on the ground & observed that the angle of elevation of the top of the tree as 36°. He then moves 50ft away from point A. In his Second position at point B, the angle of elevation of the top of the three was 22°. Find the height of the tree ?

can you also illustrate the problem and provide solution so i can properly study how to solve this equation? thankyou ​

Answer 1

18.1625 ft

Explanation:

Step 1: Calculate the height of the lower portion of the triangle (AC).

In triangle ABC, we can use the tangent function:

tan(36°) = AC / 50 ft

Rearranging the equation, we get:

AC = 50 ft * tan(36°)

Step 2: Calculate the height of the upper portion of the triangle (BC).

In triangle BAC, we can use the tangent function:

tan(22°) = h / AC

Rearranging the equation, we get:

h = AC * tan(22°)

Step 3: Substitute the value of AC from Step 1 into Step 2.

h = (50 ft * tan(36°)) * tan(22°)

Now, let's calculate the height of the tree using this formula:

h ≈ (50 ft * 0.7265) * 0.4040

h ≈ 18.1625 ft