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We are given the following details from the image:

- The span between the towers of the bridge is 80 meters.
- The arms of the bridge are raised to an angle of \( 45^\circ \).
- We need to determine the gap between the ends of the raised arms.

This is a trigonometry problem. When the arms are raised to a \( 45^\circ \) angle, the gap forms an isosceles triangle, with the raised arms acting as two sides. Each side of the triangle is half the span of the bridge (since the span is split between two arms), so each arm is \( \frac{80}{2} = 40 \, \text{m} \).

We need to find the distance between the ends of the raised arms, which is the base of the triangle formed. Using trigonometry, we apply the cosine rule or use simple geometry because the angle at the top of the triangle is \( 90^\circ - 45^\circ = 45^\circ \).

In a right triangle, the gap \( x \) can be calculated using:
\[
x = 2 \cdot (40 \cdot \sin 45^\circ)
\]
We know \( \sin 45^\circ = \frac{\sqrt{2}}{2} \), so:
\[
x = 2 \cdot (40 \cdot \frac{\sqrt{2}}{2}) = 40\sqrt{2}
\]
Approximating \( \sqrt{2} \approx 1.414 \):
\[
x = 40 \times 1.414 = 56.56 \, \text{m}
\]
This is the total distance across the gap. Since the problem asks how wide the gap is, the gap between their ends when raised will be approximately  **56.56 meters**.

However, the options provided are:

A) 23.44 m  
B) 28.44 m  
C) 18.44 m  
D) 33.44 m

This suggests there might be some oversight. Could you clarify or let me know if the options need interpretation?

The span between the towers of Tower Bridge in Sydney is 80 m. When the arms of the bridge are raised to an angle of 45°, how wide is the gap between their ends?

Solve a trigonometry problem involving Tower Bridge in Sydney, where the arms of the bridge are raised to an angle of 45°. Learn how to calculate the gap between the ends of the raised arms using trigonometric formulas. Suitable for students in Grades 9-10.

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