Question

somebody help me please

Answer 1

in triangle ABC m<B=12 degrees, m<C=32 degrees and a=32 find the lenth of b to the nearest tenth

Answer 2

@terenzreignz

Answer 3

Yeah, I'm here :)

Answer 4

Let's draw a triangle, okay?
(this is definitely not drawn to scale)

Answer 5

yay lol okay ill put up the triangle for the equation that i know how to do

Answer 6

oh there you go

Answer 7

Now, can you state the law of Sines?

Answer 8

no i dont know the law of sines

Answer 9

Okay... in a triangle, the angles are denoted by capital letters, typically A,B,and C
while the sides opposite them, by their respective lowercase letters, a,b,and c

Catch me so far?

Answer 10

yes

Answer 11

Okay, the law of Sines is as follows...
\[\huge \frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\]

Or equivalently...
\[\huge \frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}\]

Answer 12

In other words, given any triangle, the ratio between sides and the SINES of the angles opposite them is constant within the triangle.

Answer 13

okay so that can be done with the sine number on top or bottom so after we state the law of sines waht do we do next

Answer 14

Okay, we get back to your triangle...
There is still one missing angle, can you deduce what is the measure of angle A?

HINT: Remember that the sum of the measures of the interior angles of a triangle ALWAYS add up to 180 degrees :)

Answer 15

136 degreees

Answer 16

Nicely done :)


Now, the trick to these law of sines thing is to find what I call a "determining pair"

Not a very catchy name, but what I mean by a pair is one of these...
a and A
b and B
c and C

A determining pair is a pair both of whose values are given... there is such a pair in your triangle, which is it? :)

Answer 17

okay a

Answer 18

Yes, precisely, a and A
a = 32
and
A = 136 degrees

Good. Now we're supposed to find B, correct?

Answer 19

Sorry, we're supposed to find b, correct?

Answer 20

yes