Thank you for visiting A tower is 50 m high Its shadow is x meters shorter when the sun s altitude is 45 than when it is 30 Find. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
In this Mathematics problem, the concept of similar triangles and trigonometric ratios was used to find the differences in shadow lengths at two different sun altitudes. The shadow at a Sun altitude of 45 degrees was 50m. When the Sun's altitude was 30 degrees, the shadow length was 50*√3m. The difference, or 'x', thus came out to be approximately a.36.6m.
Explanation:
In Mathematics, problems like this are often solved using the properties of similar triangles. Attributes of a shadow and a triangle share certain aspects that we can apply.
First, we have to remember the concept of trigonometric ratios. For a 45-degree angle, the ratio of the height to the shadow is 1:1, meaning the shadow length is equal to the height. Therefore, when the altitude of the sun is 45°, the shadow's length is 50m.
For a 30-degree angle, the ratio of the height to the shadow is 1:√3, meaning the shadow length is √3 times the height. Therefore, when the altitude of the sun is 30°, the shadow's length is 50√3 m.
Now, to find 'x', which is how much shorter the shadow is at 45° than at 30°, we subtract the two shadow lengths: 50√3 - 50 = 50(√3 - 1). So, 'x' is approximately 36.6 m.
Learn more about Trigonometry here:
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