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The angle of elevation of the top of a tower is 38 from a point A due south of it. The angle of elevation of the top of the tower from another point B, due east of the tower is 29. Find the height of the tower if the distance from AB is 50m.

a) 25m
b) 30m
c) 35m
d) 40m

1 Answer

3 votes

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.

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