Question

Dan was curious about the height of q1 (queensland number one) and decided to measure it indirectly while he was in gold coast, australia. he used a 2 2 -meter model of the building that he found in a gift shop and measured the length of the shadow of the model to be 2.2 2.2 meters. then he measured the length of the shadow of q1 (queensland number one) and found it to be 352 352 meters. what is the height of q1 (queensland number one)?

Answer 1

Using the method of similar triangles and the measurements provided, the height of Q1 (Queensland Number One) is found by setting up a proportion and calculating the result to be approximately 320 meters.

Step-by-step explanation:

To determine the height of Q1 (Queensland Number One), Dan can use the similarity of triangles. Since the model's shadow and the Q1's shadow form similar triangles with their respective buildings, the ratio of their heights will be the same as the ratio of the lengths of their shadows. The model building is 2 meters tall with a shadow of 2.2 meters, and Q1's shadow is 352 meters. Using proportional reasoning:

• Height of model / Shadow of model = Height of Q1 / Shadow of Q1
• 2 meters / 2.2 meters = Height of Q1 / 352 meters

By cross-multiplying to solve for the Height of Q1, we get:

Height of Q1 = (2 * 352) / 2.2

This gives us:

Height of Q1 = 320 meters