Answer:
Option (1)
Step-by-step explanation:
By using triangle sum theorem in the given triangle,
(5x - 7)° + (11x - 4)° + (3x + 1)° = 180°
(5x + 11x + 3x) - (7 + 4 - 1) = 180
19x - 10 = 180
19x = 190
x = 10
Therefore, (3x + 1)° = 30 + 1
= 30°
(11x - 4)° = 110 - 4
= 106°
(5x - 7)° = 43°
Therefore, Option (1) will be the correct option.
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:
9600 sq in
Step-by-step explanation:
30 x 20 x 16 = 9600
