Final answer:
To find the height of the tower, we can use the concept of trigonometry and create two right-angled triangles, one with vertex at point A and the other with vertex at point B.
Step-by-step explanation:
To find the height of the tower, we can use the concept of trigonometry and create two right-angled triangles, one with vertex at point A and the other with vertex at point B. We can use the tangent function to solve for the height of the tower:
From the triangle with vertex at point A, tan(38°) = height of tower / distance from A to tower. So height of tower = tan(38°) * distance from A to tower.
From the triangle with vertex at point B, tan(29°) = height of tower / distance from B to tower. So height of tower = tan(29°) * distance from B to tower.
Since the height of the tower is the same in both cases, we can set these two equations equal to each other and solve for the height of the tower:
tan(38°) * distance from A to tower = tan(29°) * distance from B to tower
We know that the distance from AB is 50m. Substituting the values, we get:
tan(38°) * 50 = tan(29°) * 50
Simplifying, we get:
height of tower = tan(29°) * 50 / tan(38°)
Calculating this expression, we find that the height of the tower is approximately 35m. So, the correct answer is c) 35m.