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SAT - Math - Geometry

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. (more)

 

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and the angle AEB and the angle CBD have the same measure. What is the value of x?

∠ABE = ∠CBD (Vertically Opposity angles)

∠BEA = ∠BDC (Given)

thus triangle ABE ~ triangle CBD

thus

BE/BD = AE/CD

1400/700 = x / 800

x = 1600 ft.

 

In a right triangle, one angle measures x degrees, where sin of x degrees = 4/5. What is cos(90 degrees - x degrees)? (more)

In a right triangle, one angle measures x degrees, where sin of x degrees = 4/5. What is cos(90 degrees - x degrees)?

cos (90 - x) = sin x = 4/5

In the figure above, point O is the center of the circle, line segments LM and MN are tangent to the circle at points L and N, respectively, and the segments intersect at point M as shown. If the circumference of the circle is 96, what is the length of mi (more)

In the figure above, point O is the center of the circle, line segments LM and MN are tangent to the circle at points L and N, respectively, and the segments intersect at point M as shown. If the circumference of the circle is 96, what is the length of minor arc LN?

given

∠LMN = 60

since LM and MN are tangents

∠OLM = ∠ONM = 90

in quadrilateral ONML

∠LMN + ∠OLM + ∠ONM + ∠LON = 360

∠LON = 360 - 240 = 120

circumference of circle = 96 = 2 pi r

r = 48/pi

length of minor arc = 120/360 * 2 pi r = 1/3 * 96 = 32

Point A and B are on the surface of a sphere that has a volume (more)

Point A and B are on the surface of a sphere that has a volume of 36*pie cubic feet. What is greatest possible lenght, in feet, of line segment AB? (The volume of a sphere with radius r is V=4/3(pie)r^3.

Volume = 36 pi

4/3 pi * r3 = 36 pi

r3 = 27

r = 3

largest distance between two points on a sphere = diameter of the sphere = 2*r = 6 ft.

Point A is a vertex of an 8-sided polygon. The polygon has 8 sides (more)

Point A is a vertex of an 8-sided polygon. The polygon has 8 sides of equal length and 8 angles of equal measure. When all possible diagnols are drawn from point A in the polgygon, how many triangles are formed

A- 4
B - 5
C - 6
D - 7
E - 8

Ref to figure below, total number of triangles possible with diagonals from A would be 6