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
<span>2(p + 1) = 24
Use distributive property
2p+2=24
Subtract 2 from both sides
2p=22
Divide 2 on both sides
Final Answer: p=11</span>
Answer:
154
Step-by-step explanation:
Since its a circle, it will be 360 degrees, so then do 190+26=206, then do 360-206=154
Both graphs A and B are linear. In both graphs, the y value is going up at a constant rate in comparison to their x values. For example, in graph A every time the x value is increased by 1 the y value is increased by 2 values showing that they have the same gradient. For a graph to be linear it must have a constant rate of increase or decrease.
