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
0.25c - that’s 25% off the cost (c) of the dress
Ten to third power is 1,000 :)
Answer:
C. The 6th term is positive/negative 80
Step-by-step explanation:
Given
Geometric Progression
Required
To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;
To solve the common ratio;
Divide the 7th term by the 5th term; This gives
Divide the numerator and the denominator of the fraction by 40
----- equation 1
Recall that the formula of a GP is
Where n is the nth term
So,
Substitute the above expression in equation 1
becomes
Square root both sides
r = ±
Next, is to solve for the first term;
Using
By substituting 160 for T5 and ± for r;
We get
Multiply through by 16
Now, we can easily solve for the 6th term
Recall that the formula of a GP is
Here, n = 6;
r = ±
So,
or 
or 
or 
±80
Hence, the 6th term is positive/negative 80
Step-by-step explanation:
sec x − cos x
Secant is the inverse of cosine:
(1 / cos x) − cos x
Find the common denominator:
(1 / cos x) − (cos² x / cos x)
Subtract:
(1 − cos² x) / cos x
