Answer:
14. x=21, GK=167°, HJ=98°, HGJ=262°, GKJ=201°
15. x=9, AD=108°, BC=23°, DC=139°, DBC=221°
Step-by-step explanation:
In each case, the sum of the arcs around the circle is 360°.
__
14. 61 +(5x -7) +34 +(9x -22) = 360
14x = 294 . . . . . subtract 66, simplify
x = 21 . . . . . . . . divide by 14
(5x -7) = 98
(9x -22) = 167
- x = 21
- arc GK = 167°
- arc HJ = 98°
- arc HGJ = 360° -98° = 262°
- arc GKJ = 167° +34° = 201°
__
15. 90 +(2x +5) +(17x -14) +(12x) = 360
31x = 279 . . . . subtract 81, simplify
x = 9 . . . . . . . . divide by 31
(2x+5) = 23
(17x -14) = 139
(12x) = 108
- x = 9
- arc AD = 108°
- arc BC = 23°
- arc DC = 139°
- arc DBC = 360° -139° = 221°
It might be hard at first to find the hundreds place. The answer is C:722,357,000
Answer:
- sin(X) = 6/7.5
- XY = 4.5
- cos(X) = 4.5/7.5
- tan(X) = 6/4.5
Step-by-step explanation:
It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...
XZ² = YZ² + XY²
Solving for XY, you find ...
XY² = XZ² - YZ²
XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25
XY = 4.5
The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...
Sin = Opposite/Hypotenuse
sin(X) = 6/7.5
Cos = Adjacent/Hypotenuse
cos(X) = 4.5/7.5
Tan = Opposite/Adjacent
tan(X) = 6/4.5
_____
<em>Comment on the triangle and ratios</em>
The side lengths of this triangle are in the ratios ...
XY : YZ : XZ = 3 : 4 : 5
If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.
The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.
Answer:
i am not sure but i thinks 2-1 is 1
Step-by-step explanation:
