Which of the following is acceptable justifications to use in geometry when justifying statements about segments and
1 answer:
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Answer:
1) The windsurfer is approximately 580 ft from each lifeguard stand.
2) The distance between the Earth and Mercury is approximately 61 million miles.
Step-by-step explanation:
The image other two situations described is presented in the attached image to this answer.
1) From the attached image, the windsurfer forms a right angled triangle with each of the lifeguard stand and the midpoint between the two lifeguard stands.
Hence, the angle at the top of the triangle is half of 30°, 15° and the distance from the midpoint of the lifeguard stands to the lifeguard stands is 300/2 = 150 ft.
Let the required distance of the windsurfer from each of the lifeguard stands be x.
Using trigonometric relations,
Sin 15° = (150/x)
x = 150 ÷ sin 15° = 150 ÷ 0.2588
x = 579.6 ft = 580 ft to the nearest whole number
2) From the image, the Sun, Earth and Mercury form a triangle.
Let the possible distance between the Earth and Mercury be y.
Using cosine rule,
y² = 36² + 93² - (2×36×93×cos 22°)
y² = 3,736.5769098208
y = √3,736.5769098208 = 61.13 million miles = 61 million miles to the nearest million miles.
Hope this Helps!!!
So, this is a proportion problem. If we express 75% as a fraction (3/4ths), we have:
Since he won all of his games, we add the number won (x), to the number previously won and divide it by the total games played which is just the previous games played plus the number of current games played, so since he lost no games we still add x to the denominator as well. Solving this gives us:
That x value is 20.