Question

The angle of elevation to the top of a television tower is 45 degrees from each of the two points. The points are 60cm apart one due south and other due east of the tower.What is the height of the tower

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let the height of the tower be h cm.

From the given information, we can create a right-angled triangle with the height of the tower as the opposite side, the distance between the two points as the adjacent side, and the angle of elevation as 45 degrees.

Using trigonometry, we can find the height of the tower:
tan(45 degrees) = height / distance between the two points
tan(45 degrees) = h / 60
1 = h / 60
h = 60 cm

Therefore, the height of the tower is 60 cm.

Answer 2

the line joining the two points is 60 cm long, and runs southeast.

Therefore, the two perpendicular lines joining the points has length 60/√2 = 30√2
Now we can see that the height h is also 30√2 cm

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the oversight. Thank you for pointing that out.

Given that the distance between the two points is 60 cm and runs southeast, we can calculate the length of the perpendicular lines joining the points:

60 cm / √2 = 30√2 cm

Therefore, the height of the tower (opposite side) is also 30√2 cm. Hence, the correct height of the tower is indeed 30√2 cm. Thank you for the correction.