Answer:
a = √11 and b = 6
Step-by-step explanation:
Refer to attached picture for reference
for an right triangle with angle θ
we are given
cos θ = 5/6 = length of adjacent side / length of hypotenuse
hence
adjacent length = 5 units
hypotenuse length = 6 units
the missing side is the "opposite" length which we can find with the Pythagorean equation. in our case:
hypotenuse ² = adjacent ² + opposite² (rearrange)
opposite ² = hypotenuse ² - adjacent ²
opposite ² = 6² - 5²
opposite = √ (6²-5²) = √11
sin θ = opposite length / hypotenuse (substitute values above)
sin θ = √11 / 6
hence a = √11 and b = 6
Answer:
Step-by-step explanation:
The equation of a circle:
<em>(h, k)</em><em> - center</em>
<em>r</em><em> - radius</em>
<em />
We have diameter endpoints.
Half the length of the diameter is the length of the radius.
The center of the diameter is the center of the circle.
The formula of a distance between two points:
Substitute the coordinates of the given points (-8, 2) and (-2, 6):
The radius:
The formula of a midpoint:
Substitute:
Finally:
Approx - 10%
72 students signed up for canoeing + the 23 students who signed up for trekking + the 13 students who signed up for both = 108 students
there are 120 students total, so you have to subtract 120 - 108 = 12
Now to find the percentage, you have to divide the number of students who didn't sign up for either, by the total
which is .1 = 10/100 = 10%
2x + 100 = 5x + 55
3x = 45
x = 15
2(15) + 100 = 130
180-130 = 50
so angle 2 is 50 degrees
6(-3)-1-51+131=
-18-1-51+131=
-70+131=61
