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:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown".
Step-by-step explanation:
In x + 2 = 7, x is a variable, but we can work out its value if we try:)
Answer:
D
Step-by-step explanation:
6(x + 8) = Plug in x with 4
6(4 + 8) =
6(12) =
72
to see quick score she must use a pie chart
Answer:
the number of hamburgers sold on Thursday were 325.
Step-by-step explanation:
The total number of hamburger and cheese burger is missing
i will replace it with any figure, you can replace it wit your given data and you will get the solution.
A local hamburger shop sold a combined total of 593 hamburgers and cheeseburgers on Thursday
There were 57 fewer cheeseburgers sold than hamburgers
How many hamburgers were sold on thursday
Let h be the number of hamburgers and c be the number of cheeseburgers.
Using this information we can set up two equation as:
Now we need to solve these two equations to get the value of number of hamburgers. For that we use substitution method as shown below:
Therefore, the number of hamburgers sold on Thursday were 325.
