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Margaret [11]
3 years ago
8

Select all true statements.

Mathematics
1 answer:
andrey2020 [161]3 years ago
5 0

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)

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