Solve each problem. Height of a Lunar Peak The lunar mountain ...

Question

Solve each problem. Height of a Lunar Peak The lunar mountain peak Huygens has a height of 21,000 ft. The shadow of Huygens on a photograph was 2.8 mm, while the nearby mountain Bradley had a shadow of 1.8 mm on the same photograph. Calculate the height of Bradley. (Data from Webb, T., Celestial Objects for Common Telescopes, Dover Publications.)

Accepted Answer

Welcome back. Everyone in this problem. We're talking about two skyscrapers named Rivers and Everlast in an alien world. The building rivers stands 1500 m tall and its shadow in a picture is 2.4 centimeters. Meanwhile, the closest skyscraper ever lasts casts a shadow of 1.5 centimeters on the same picture. Assuming that the angles of sunlight are similar for both skyscraper peaks and that the picture was taken under consistent lighting conditions. What is the height of Everlast for our answer choices? A is 2400 m. B is 417.5 m. C is 937.5 m and D is 1250 m. Now, let's try to draw our problem to make sense of it. So we're talking about some buildings in a picture, some alien buildings like that. And in our problem, it says that we have one skyscraper named Rivers. So I'll draw it right here and I'll call this building R and another skyscraper called Everlast. I'll call this building E we know that Rivers stands 1500 m tall. So I'll put that on my diagram and we also know that rivers has a shadow in the picture that is 2.4 centimeters. So if they were measuring it in the picture, it prob it would have probably looked something like this. We also know that for ever last, we don't know how tall it is. We don't know its height. OK. But we do know that the length of its shadow, the length of its shadow is 1. centimeters. And let me put in the 2.4 centimeters for rivers. So since we know that we're trying to figure out the height of the building ever lasts, no notice that our problem tells us the angles of sunlight are similar for both skyscraper peaks. Ok? So the angle of sunlight are similar and the picture was taken under consistent lighting conditions and it's the same picture. So it stands to reason then that whatever the length of the shadow in the picture for the building rivers, it would be proportional to the length of the shadow for the building Everlast and its height. So that tells us then if we think about it, the ratios make a note of that. So the ratios of the shadow to the height of each building re in other words, since they're proportional the ratio of the shadow to the height of, so let's write shadow, let's let s with the length of the shadow length of shadow in picture. Ok. Let me write that up properly length of shadow in the picture. And let's let each with the length of the skyscraper length of the skyscraper. Ok. Then what this tells us is that the ratio of the height of Everlast to its shadow in the picture must be equal to the height of rivers to the shadow of rivers in the picture. And the good thing is we know the height of building rivers, we know the length of its shadow. And we also know the length of the shadow of Everlast. So we can use that to help us find out how tall the Everlast building is. Now, that means that the height of Everlast two, the length of its shadow, which is 1.5 centimeters equals the height of rivers, which is 1500 m to the length of its shadow, which is 2.4 centimeters. That means then that the height of Everlast. If we multiply both sides by 1.5 the height of building Everlast will be 1500 multiplied by 1. all divided by 2.4 centimeters. Now, if you were to put that in your calculator, you'll find that the height of building Everlast equals 937.5 m. When we look back in our answer choices, that would have been answer choice. C thanks a lot for watching everyone. I hope this video helped

Key Concepts

Similar Triangles and Proportionality

Ratio and Proportion

Unit Consistency and Conversion

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