Question

Select all true statements.

Answer 1

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

Explanation:

Here, in the given triangle ABC

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

Now, by Trigonometric Functions:

`(Sin A)/(8) = (Sin B)/(16) =(Sin C)/(20)`

Comparing first two terms, we get:

`(Sin A)/(8) = (Sin B)/(16) \\\implies 2Sin A = Sin B` ........... (1)

Also,

`(Sin B)/(16) = (Sin C)/(20) \\\implies Sin C = 1.25 Sin B` ....... (2)

Comparing first and last terms, we get:

`(Sin C)/(20) = (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)