Question

Pls help:Find all the missing elements:

Answer 1

B = 48.7° , C = 61.3° , b = 12

Explanation:

In order to find B we must first angle C

To find angle C we use the sine rule

That's

`( |a| )/( \sin(A) ) = ( |c| )/( \sin(C) )`

From the question

a = 15

A = 70°

c = 14

So we have

`(15)/( \sin(70) ) = (14)/( \sin(C) )`

`\sin(C) = (14 \sin(7 0 ) )/(15)`

`C = \sin^( - 1) ( (14 \sin(70) )/(15) )`

C = 61.288

C = 61.3° to the nearest tenth

Since we've found C we can use it to find B.

Angles in a triangle add up to 180°

To find B add A and C and subtract it from 180°

That's

A + B + C = 180

B = 180 - A - C

B = 180 - 70 - 61.3

B = 48.7° to the nearest tenth

To find b we can use the sine rule

That's

`( |a| )/( \sin(A) ) = ( |a| )/( \sin(B) )`

`(15)/( \sin(70) ) = ( |b| )/( \sin(48.7) )`

`|b| = (15 \sin(48.7) )/( \sin(70) )`

b = 11.9921

b = 12.0 to the nearest tenth

Hope this helps you