Find the value of x if a, b, and c are collinear points and b is between a and c. ab=12,bc=5x−2,ac=3x 20
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Answer:
An equation that represents the given situation is and the additional number of students that can be seated is 47
Step-by-step explanation:
Number of students already seated in school cafeteria = 203
Let x be the additional number of students that can be seated
So, Total number of seats available in school cafeteria = 203+x
We are given that the school cafeteria seats 250 students
So, 203+x=250
Hence an equation that represents the given situation is and the additional number of students that can be seated is 47
The height of the smaller building is <u>94.63 feet</u>, computed using the trigonometric ratios.
In the question, we take AB to be the taller building, where A is its top and B is its base, CD to be the shorter building, where C is its top and D is its base, and CE to be the perpendicular from C to AB.
Given that the horizontal distance between the two buildings is 260 feet, we can say that BC = CE = 260 feet.
The angle of elevation from the top of the shorter building to the top of the taller building is 30°, that is, ∠ECA = 30°.
The angle of depression from the top of the shorter building to the base of the taller building is 20°, that is, ∠ECB = 20°.
When ∠ECB = 20°, then ∠CBD = 20°, as they are alternate angles.
We are asked to find the height of the shorter building, that is, we are asked to find CD.
In ΔCBD,
tan ∠CBD = CD/BD {perpendicular/base},
or, tan 20° = CD/260,
or, CD = 260*tan 20° = 260*0.36397023426 {∵ tan 20° = 0.36397023426},
or, CD = 94.6322609092.
Therefore, the height of the smaller building is <u>94.63 feet</u>, computed using the trigonometric ratios.
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