AB = 6 cm, AC = 12 cm, CD = ?
In triangle ABC, ∠CBA = 90°, therefore in triangle BCD ∠CBD = 90° also.
Since ∠BDC = 55°, ∠CBD = 90°, and there are 180 degrees in a triangle, we know ∠DCB = 180 - 55 - 90 = 35°
In order to find ∠BCA, use the law of sines:
sin(∠BCA)/BA = sin(∠CBA)/CA
sin(∠BCA)/6 cm = sin(90)/12 cm
sin(∠BCA) = 6*(1)/12 = 0.5
∠BCA = arcsin(0.5) = 30° or 150°
We know the sum of all angles in a triangle must be 180°, so we choose the value 30° for ∠BCA
Now add ∠BCA (30°) to ∠DCB = 35° to find ∠DCA.
∠DCA = 30 + 35 = 65°
Since triangle DCA has 180°, we know ∠CAD = 180 - ∠DCA - ∠ADC = 180 - 65 - 55 = 60°
In triangle DCA we now have all three angles and one side, so we can use the law of sines to find the length of DC.
12cm/sin(∠ADC) = DC/sin(∠DCA)
12cm/sin(55°) = DC/sin(60°)
DC = 12cm*sin(60°)/sin(55°)
DC = 12.686 cm
Answer:
D.) (5, 3)
Step-by-step explanation:
Solution is where two lines intersect
Both lines intersect at x = 5 and y = 3
Answer
D.) (5, 3)
Answer:
-5x + 56
Step-by-step explanation:
Use distributive property to refine.
20 - 2x + 36 - 3x
Combine Like Terms
-5x + 56
Answer:
x^2 + 8x + 16
Step-by-step explanation:
(x + 4) (x+ 4) multiply x by x and x by 4.
x^2 + 4x
Then multiply 4 by x and 4 by 4.
4x + 16
Then combine like terms.
x^2 + 4x + 4x +16
x^2 + 8x + 16
Yes i believe thats it ok
