Answer:
The perimeter of ΔABC is 43 units
Step-by-step explanation:
An illustrative diagram is shown in the attachment below.
To find the perimeter of the triangle, we will first determine the length of the unknown sides.
First, we can determine /BC/ using the Sine rule
From Sine rule
[tex]\frac{SinA}{a} = \frac{SinB}{b} = \frac{SinC}{c}[/tex]
∴ [tex]\frac{SinA}{a} = \frac{SinC}{c}[/tex]
In the diagram, [tex]a = /BC/[/tex] and [tex]c = /AB/ = 12[/tex]
m∠A=60° and m∠C=45°
∴ [tex]\frac{Sin60}{/BC/} = \frac{Sin45}{12}[/tex]
[tex]/BC/ = \frac{12 \times Sin60}{Sin45}[/tex]
[tex]/BC/ = 6\sqrt{6}[/tex]
To find /AC/, will first determine m∠B
m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)
60° +m∠B + 45° = 180°
m∠B + 105° = 180°
m∠B = 180° - 105°
m∠B = 75°
Also, using the sine rule
[tex]\frac{SinB}{b} = \frac{SinC}{c}[/tex]
From the diagram, [tex]b = /AC/[/tex]
[tex]\frac{Sin75}{/AC/} = \frac{Sin45}{12}[/tex]
[tex]/AC/ = \frac{12 \times Sin75}{Sin45}[/tex]
[tex]/AC/ = 6 + 6\sqrt{3}[/tex]
Now,
The perimeter of ΔABC = /AB/ + /BC/ + /AC/
= [tex]12 + 6\sqrt{6} + 6+6\sqrt{3}[/tex]
= 43.09 units
≅ 43 units
Hence, the perimeter of ΔABC is 43 units.
Answer:
Using the figure above, if AB = RT and ∠R = 70°, then ________.
ΔABC ~ ΔRTS
m ∠ S = 50°
ΔABC ≅ ΔRTS
m ∠ S = 60°
Step-by-step explanation:
