D. (-2, 0, 1, 3)
x-intercepts are where the line touches the horizontal line (x-axis)
This is the concept of trigonometry and its identities;
We are required to calculate the length of the kite's diagonals;
Here we use the trigonometric identities;
let theta=x
tan x=opposite/adjacent
opposite=17
adjacent=10
thus
tan x=17/10
x=tan^-1 17/10
x=59.54
Therefore half the length of the diagonal will be given by:
sin x=h/10
h=10 sin x
h=10 sin 59.54
h=8.62
thus the length of the diagonal will be:
2*8.62
=17.24 in
<h2>sum of angle of triangle is 180°</h2>
<h2>A+B+C = 180 </h2>
<h2>38°+75°+ X = 180°</h2>
<h2>113° + X = 180°</h2>
<h2>X = 180° -113</h2>
<h2>X = 67°</h2>
Step-by-step explanation:
h = height of rectangle (should be "length", but ok)
w = width of rectangle
w = h + 97
the diagonal of the rectangle is the Hypotenuse (baseline) of a right-angled triangle with the legs being one height and one width side of the rectangle.
so, we use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle).
diagonal² = h² + (h + 97)² = h² + h² + 2×97h + 97²
113² = 12769 = 2h² + 194h + 9409
3360 = 2h² + 194h
1680 = h² + 97h = (h + 97/2)² - 9409/4
(completing the square)
6720/4 + 9409/4 = (h + 97/2)²
16129/4 = (h + 97/2)²
127/2 = h + 97/2
30/2 = h = 15
the height is 15.0 in
