Determine whether each triple
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Chapter 5 Solutions
Elementary Geometry For College Students 7e
- (ii)arrow_forwardA convex polygon is said to be regular if all of its sides have the same length and all angles between sides are the same. Let Pr denote the regular convex n-sided polygon. Thus, P3 is the equilateral triangle, P₁ is the square, P is the pentagon etc. Compute a formula for the size of any internal angle of Pn.arrow_forward+ Recall that a map, f: R2 R², is an isometry if |P-Q| = |ƒ(P) — ƒ (Q) for all pairs of points P and Q in R². Thus, f is a distance preserving map. Show that an isometry, f: R² → R² also preserves angles. In other words if two line segments meeting at a point determine an angle a, their image line segments meeting at the image of that point also determine the angle a.arrow_forward
- Using Harriott's formula for the area of a triangle on the unit sphere, S2, compute the Euler characteristic X(S2). Make sure to explain what the Euler characteristic is. (The point of the exercise is to show that this notion is well-defined.)arrow_forwardProve Harriot's Formula (Area of a Triangle on a Sphere).arrow_forwardIn rhombus ABCD, diagonals BD¯¯¯¯¯¯BD¯ and AC¯¯¯¯¯AC¯ intersect at point E. If BE = 4n – 3 and EC = 2n + 5, which expression can be used to represent AD?arrow_forward
- Prove that the image of a polygon in R², under an isometry, is congruent to the original polygonarrow_forward9 AB is parallel to plane m and perpendicular to plane r. CD lies in r. Which of the following must be true? arim br m 6 CD L m d AB || CD e AB and CD are skew.arrow_forward(6) Prove that the image of a polygon in R², under an isometry, is congruent to the original polygon.arrow_forward
- sat Pie Joday) B rove: ABCB. Step 1 Statement D is the midpoint of AC ED FD ZEDAZFDC Reason Given 2 ADDC Select a Reason... A OBB hp B E F D Carrow_forward6) Find the area of the shaded region. Leave your answer in terms of π. A 2 B C A) 16.5л B) 30д 3.1988 C) 3л π D) 7.5π 9.+2uarrow_forwardTask number: A1.1, A1.7 Topic: Celestial Navigation, Compass - Magnetic and Gyro Activ Determine compass error (magnetic and gyro) using azimuth choosing a suitable celestial body (Sun/ Stars/ Planets/ Moon). Apply variation to find the deviation of the magnetic compass. Minimum number of times that activity should be recorded: 6 (2 each phase) Sample calculation (Azimuth- Planets): On 06th May 2006 at 22h20m 10s UTC, a vessel in position 48°00'N 050°00'E observed Mars bearing 327° by compass. Find the compass error. If variation was 4.0° East, calculate the deviation. GHA Mars (06d 22h): Increment (20m 10s): 089° 55.7' 005° 02.5' v (0.9): (+) 00.3' GHA Mars: 094° 58.5' Longitude (E): (+) 050° 00.0' (plus- since longitude is easterly) LHA Mars: 144° 58.5' Declination (06d 22h): d (0.2): N 024° 18.6' (-) 00.1' Declination Mars: N 024° 18.5' P=144° 58.5' (If LHA<180°, P=LHA) A Tan Latitude/ Tan P A Tan 48° 00' Tan 144° 58.5' A = 1.584646985 N (A is named opposite to latitude, except when…arrow_forward
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