Question

Select all true statements.

Answer 1

Answer:

A) Sin A  + Sin B  =  1.2 Sin C  

D) Sin C =  2.5 Sin A  = 1.25 Sin B

E)  Sin A  + Sin C  =  1.75 B

Step-by-step explanation:

Here, in the given triangle ABC

Base AC = 16 units, AB  = 2 units, and BC  = 8 units

Now, by Trigonometric Functions:

$\frac{Sin A}{8} = \frac{Sin B}{16} =\frac{Sin C}{20}$

Comparing first two terms, we get:

$\frac{Sin A}{8} = \frac{Sin B}{16} \\\implies 2Sin A = Sin B$                 ........... (1)

Also,

$\frac{Sin B}{16} = \frac{Sin C}{20} \\\implies Sin C = 1.25 Sin B$   ....... (2)

Comparing first and last  terms, we get:

$\frac{Sin C}{20} = \frac{Sin A}{8} \\\implies SinC = 2.5 Sin A$      ..........  (D)

Also, Sin A  = 0.5 Sin B

So, the given statement Sin A  = 2 Sin B is FALSE

⇒ 2.5 Sin A  = 1.25 Sin B   .......... (D)

Also,  Sin B  = 2 Sin A

⇒ Sin A  + Sin B =  Sin A + 2 Sin A =  3 Sin A

Also, Sin A  = 0.4 Sin C

⇒3 Sin A = 3 x (0.4) Sin C  = 1.2 Sin C  ..

⇒Sin A  + Sin B  =  1.2 Sin C   ........ (A)

B)   Sin A  - Sin B  = 0.4 Sin C - 2 Sin A  =  0.4 Sin C - 2 (0.4 Sin C)  

= 0.4 Sin C  - 0.8 Sin C  = -0.4 Sin C

⇒Sin A  - Sin B  =  -0.4 Sin C   ........ (B)

So, the given statement is FALSE

E)   Sin A  + Sin C =  0.5 Sin B + 1.25 B =  1.75 B

⇒ Sin A  + Sin C  =  1.75 B  ....(E)