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3 years ago

1. Define Line, Line segment and Ray.

Mathematics

2 answers:

weqwewe [10]3 years ago

8 0

Answer:

Line :-

A line is defined as a line of points that extends infinitely in two directions. It has one dimension, length. Points that are on the same line are called collinear points.

Line segments :-

A straight line which links two points without extending beyond them. The points P and Q are called the 'endpoints' of the segment. ... The word 'segment' typically means 'a piece' of something, and here it means the piece of a full line, which would normally extend to infinity in both directions.

Ray :-

A part of a line with a start point but no end point (it goes to infinity) Try moving points "A" and "B": line.

Complementary Angles :-

Two Angles are Complementary when they add up to 90 degrees (a Right Angle). They don't have to be next to each other, just so long as the total is 90 degrees. Examples: ... 5° and 85° are complementary angles.

Supplementary Angles:-

Two Angles are Supplementary when they add up to 180 degrees. They don't have to be next to each other, just so long as the total is 180 degrees. Examples: • 60° and 120° are supplementary angles.

Adjacent Angles :-

Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap. Angle ABC is adjacent to angle CBD. Because: they have a common side (line CB).

Linear Pair :-

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Transversal lines :-

In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether two other lines in the Euclidean plane are parallel.

Corresponding angles :-

Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

Step-by-step explanation:

vitfil [10]3 years ago

4 0

Answer:

A line is a straight path of points that has no beginning or end

A line segment is a portion of a line that has two endpoints

A ray is a portion of a line which has one endpoint and extends forever in one direction

Complementary angles are two angles whose sum adds up to 90 degrees

Supplementary angles are two angles that add up to 360 degrees

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Juan and Nina are in the Junior High Orchestra. As part of the orchestra they each have to learn two instruments. Juan is learni

Whitepunk [10]

Answer:

Nina practiced the viola for 11.25 hours last week.

Step-by-step explanation:

Juan practiced the violin for 9 hours last week. For each 3 hours that he practices the violin, he practices 2.5 hours of cello. So

3h violin - 2.5h cello

9h violin - xh cello

$3x = 9*2.5$

$x = 7.5$

He practiced 7.5 hours of cello, the same as Nina.

For every 3 hours Nina spends practicing the viola she practices the cello for 2 hours. So:

3h viola - 2h cello

xh viola - 7.5h cello

$2x = 3*7.5$

$x = 7.5*1.5$

$x = 11.25$

Nina practiced the viola for 11.25 hours last week.

3 0

3 years ago

Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .