Answer:
C) 405.3 ft
Step-by-step explanation:
A triangle is a polygon with three angles and three sides. Types of triangle are scalene, isosceles, equilateral, right angled triangle.
Given a triangle with angles A, B, C and the corresponding sides directly opposite to the angles as a, b, c. The sine rule states that:
![\frac{a}{sin(A)}= \frac{b}{sin(B)} =\frac{c}{sin(C)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%3D%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20%3D%5Cfrac%7Bc%7D%7Bsin%28C%29%7D)
In the triangle formed by point C, ship B and ship A, we have ∠A = 82°, ∠B = 78°, c = AB = 140 ft. Hence:
∠A + ∠B + ∠C = 180° (sum of angles in a triangle)
82 + 78 + ∠C = 180
∠C + 160 = 180
∠C = 20°
Using sine rule:
![\frac{c}{sin(C)}=\frac{a}{sin(A)}\\\\\frac{140}{sin(20)}=\frac{a}{sin(82)}\\\\a= \frac{140*sin (82)}{sin(20)}\\\\a=405.3\ ft](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Bsin%28C%29%7D%3D%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%5C%5C%5C%5C%5Cfrac%7B140%7D%7Bsin%2820%29%7D%3D%5Cfrac%7Ba%7D%7Bsin%2882%29%7D%5C%5C%5C%5Ca%3D%20%20%20%20%5Cfrac%7B140%2Asin%20%2882%29%7D%7Bsin%2820%29%7D%5C%5C%5C%5Ca%3D405.3%5C%20ft)
a = distance from Ship B to the signal fire at point C
Answer:
5 eggs.
Step-by-step explanation:
Well, 3/4 of 12 is 9 and 5/6 of 12 is 10. So, 12 - 9 = 3 and 12 - 10 = 2
Therefore, Matthew has 5 eggs left over.
I hope I helped ^^
The 3 angles need to equal 180 when added together:
A) 49 + 59 +72 = 180
The others do not equal 180
A pair of numbers is a solution of y = -3x if the second number, y, is -3 times the first number, x.
What about the pair (-1, 4)? If you replace x with -1, you get y = -3(-1) = 3, not 4. So (-1, 4) is NOT a solution.
For each answer choice, you have to check all three of the given pairs.
(0, 0) is a solution because if x = 0, then y = -3(0) = 0.
(3, -9) is a solution because if x = 3, then y = 3(-3) = -9.
Can you finish it?
(n+7)2
= (n)(2) + (7)(2)
=2n+14