Right △EFG has its right angle at F, EG=8, and FG=6.

What is the value of the trigonometric ratio of an angle of the triangle?

I. sec G = 4/3

II. cot G = (3√7)/7

III. sin E = ¾

Step-by-step explanation:

Given

Right angled triangle

EG = 8

FG = 6

Required

sec G

cot G

sin E

First, the length of the three sides of the triangle must be completed.

From the attachment below, we can deduce that (by using Pythagoras theorem)

Hyp² = Adj² + Opp²

EG² = FG² + EF²

Substitute  EG = 8 and FG = 6

8² = 6² + EF²

64 = 36 + EF²

Collect like terms

EF² = 64 - 36

EF² = 28

Take square root of both sides

√EF² = √28

EF = √28

EF = √(4 * 7)

EF = √4 * √7

EF = 2 * √7

EF = 2√7.

Now, the trigonometric functions can be solved.

i. sec G.

sec is the reciprocal of cos .

So, we need to solve first for cos G

cos G = Adj/Hyp

Here, adj = 6 and hyp = 8

So,

cos G = 6/8

cos G = ¾

So,

sec G = 1/(¾)

sec G = 4/3

ii. cot G

cot is the reciprocal of tan

So, we need to solve first for tan G

tan G = Opp/Adj

Here, adj = 6 and opp = 2√7

So,

tan G = 2√7/6

tan G = √7/3

So,

cot G = 1/(√7/3)

cot G = 3/√7

Rationalise

cot G = 3/√7 * √7/√7

cot G = (3√7)/7

iii. sin E

sin E = Opp/Hyp

Here, Opp = 6

Hyp = 8

So,

sin E = 6/8

sin E = ¾

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is