Answer:
Step-by-step explanation:
-1 is the answer hope that helps :D
∠A = 36
∠C =36
∠ADB =72°
∠CBD =36°
∠BDC =108°
Explanation:
AB=AD then ∠ABD & ∠ADB must be equal as they share two lines that are equal so ∠ADB=72°
∠A and ∠C must also be equal (AB=BC)
∠A = 180-72-72=36°
So ∠A & ∠C=36°
∠D=180° (straight line)
So if ∠ADC=72
∠BDC=108° (180-72)
A triangle has 180° so in triangle BDC we have 108° and 36°
So remaining angle (∠CBD) =180-108-36
=36°
This tells us that triangle BDC is isosceles as it has two equal angles ∠CBD & ∠C =36°
Answer:
The coordinates of B is (3, - 5)
Step-by-step explanation:
A(6, 1)
C(2, -7)
Coordinates of point B such that AB = 1/3 × BC
Hence we have;
Therefore BC = 3/4 × AC
Hence, AB = 1/3 × BC = 1/3 × 3/4 × AC = 1/4 × AC
AC = √((6 - 2)² + (1 - (-7))²) = √(16 + 64) = √80 = 4·√5
AB = 1/4 × 4·√5 = √5
Therefore;
AB² = (x - 6)² + (y - 1)² = 5
Slope = (1 - (-7))/(6 - 2) = 2
Hence the y coordinate of B = -7 + sin(tan⁻¹(2)) ×√5 = -5
The x coordinate of B = 2 + cos(tan⁻¹(2)) ×√5 = 3
The coordinates of B = (3, - 5)
Answer:
C. 3Pi/2 or 270 degrees
Step-by-step explanation:
The first step is to ignore the negative sign and then evaluate the arcsin of 1 to obtain the reference angle of θ in the first quadrant;
θ = arcsin(1)
θ = 90 degrees or equivalently pi/2
Since the sine of θ was given as -1, this will imply that θ lies either in the third or forth quadrant where the sine of an angle is negative.
To obtain the value of θ in the third quadrant we simply add 180 degrees of pi radians to our reference angle;
90 + 180 = 270 degrees
pi/2 + pi = 3/2 pi
