Answer:
DE ≈ 14.91
Step-by-step explanation:
Make use of the relationships between sides and angles in a right triangle. These are summarized by the mnemonic SOH CAH TOA:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
__
The side DE is opposite the angle 19°, so the sine or tangent relation will be involved. The sine relation requires you know hypotenuse EF. The tangent relation requires you know adjacent side DF.
The only common side between triangles CDF and DEF is side DF. That side is opposite the given 61° angle. The given side length (CF = 24) is adjacent to the 61° angle.
This means you have enough information to use these relations:
tan(61°) = DF/CF = DF/24
DF = 24·tan(61°)
and
tan(19°) = DE/DF
DE = DF·tan(19°) = (24·tan(61°))·tan(19°) . . . . . use DF from above
DE ≈ 24(1.804048)(0.344328) ≈ 14.908
The length of DE is about 14.91.
We have measures of all tree sides of the both triangles,
so we can use SSS to check if the triangles are similar.
|ED|/|AB| =5/10=1/2
|DC|/|BC| = 4/8 = 1/2
|EC|/|AC| = 6/12 = 1/2
We see that all tree pairs are in proportion, so these triangles ΔABC and ΔEDC are similar.
We have enough information to prove that ΔABC similar to ΔEDC.
The ratio of the number of female attendants to the number of male attendants is 21/17
<h3>Ratio</h3>
- Amount donated by female attendant = $1200
- Amount donated by male attendant = $800
- Average donation = $900
let
- number of female attendant = x
- number of male attendant = y
900 = 1200x + 800y / (x + y)
900x + 900y = 1200x + 800y
900x + 1200x = 800y + 900y
2100x = 1700y
x : y = 2100 / 1700
x : y = 21 ; 17
Learn more about ratio:
brainly.com/question/2784798
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Answer:
$1.85
Step-by-step explanation:
2.15
-1.30
--------
1.85
Answer:
D.
Step-by-step explanation:
The line crosses the y-axis at (0,5), so we immediately eliminate B. The section of the line that is increasing begins when x is 10 and stops increasing when x is 2
