For the triangles abc and mnp m∠a = m∠m, ab = 16, ac = 10, mn = 7, mp = 24. find the ratio of the a△mnp and a△abc .

21 : 20

Step-by-step explanation:

Area of ABC

½ × AB × AC sinA

½ × 16 × 10 sinA

80sinA

Area of MNP

½ × MN × MP sinM

sinM = sinA because angle M = angle A

½ × 7 × 24 sinA

84sinA

Ratio:

MNP : ABC

84sinA : 80sinA

21 : 20

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: