So what you are looking for is the hypotenuse of the triangle DCF.
We know DC is 3cm, so we need CF.
BC and CF and CF create a right triangle.
Using Pythagorean Theorem, CF is about 10.2
Now using Pythagorean Theorem again, 3^2 +10.2^2=113
The sqaureroot of that is 10.6. So 10.6 is your answer
Answer:
-7x + 4y = +42
Step-by-step explanation:
Going from point (2, -7) to point (6, 0), x increases by 4 and y increases by 7. Thus, the slope of the line in question is m = 7/4.
Starting from the equation y = mx + b, and subbing (7/4) for m, 6 for x and 0 for y, we get:
0 = (7/4)(6) + b. Then b = 42/4, or 21/2. Thus, we now have y = (7/4)x + 21/2.
We must put this into "standard form." Multiplying all three terms by 4, we get:
4y = 7x + 42. Rearranging these terms to fit the "standard form" equation Ax + By = C, we get:
-7x + 4y = +42
A=43°
B=82°
c=28
1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)
2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°
2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3
2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
b=28 sin 82° / sin 55°
Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8
Answer: Option B) C=55°, b=33.8, a=23.3
297,000,000 is your answer.
