In Triangle ABC, a=15cm, c=9cm, and angle C= 35 degrees. Find b and angle b. (Recall sin theta= sin (180 degrees-theta). I'm not sure how to approach this.

Question

In Triangle ABC, a=15cm, c=9cm, and angle C= 35 degrees. Find b and angle b. (Recall sin theta= sin (180 degrees-theta). I'm not sure how to approach this.

Answer 1

you have C and c and a, so you can find A using

sinA/a = sinC/c

Now, having A and C, you know that A+B+C=180, so you can easily find B.

Then, use the law of sines again to get b:

b/sinB = c/sinC = a/sinA

Answer 2

sin A/15 = sin 35/9 = .0637

sin A = .956

so A = 72.9 degrees or 180-72.9 = 107.1
then A + B + C = 180
72.9 + B + 35 = 180
B = 72.1 degrees (One answer)
sin B/b = .0637
so b = 14.94
or
A = 107.1
then B = 180 - 35 -107.1 = 37.9 degrees (alternate answer)

Answer 3

Thanks! I should have mentioned this in the question, but the answer sheet asks for two values of angle A rather than 1.

Answer 4

Oh nvm thanks Damon.

Answer 5

And steve sorry I didn't read the whole answer.

Answer 6

To find side b and angle B in Triangle ABC, you can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant. In other words, it states:

a / sin A = b / sin B = c / sin C

Given that a = 15cm, c = 9cm, and angle C = 35 degrees, we can start by finding angle A. To calculate angle A, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Angle A + Angle B + Angle C = 180 degrees
Angle A + Angle B + 35 degrees = 180 degrees
Angle A + Angle B = 180 degrees - 35 degrees
Angle A + Angle B = 145 degrees

Now we can apply the Law of Sines using side a and angle A:

15cm / sin A = b / sin B

To find the missing side b, we isolate it in the equation, but firstly we need to find angle B. We can use the relationship mentioned in the question:

sin B = sin (180 degrees - B)

So, we can rewrite the equation as:

15cm / sin A = b / sin (180 degrees - B)

Substituting the known values, we have:

15cm / sin A = b / sin (180 degrees - B)
15cm / sin A = b / sin (145 degrees) [since A + B = 145 degrees]

And now we solve for b:

b = (15cm / sin A) * sin (145 degrees)

To calculate sin A, we can use the relationship mentioned in the question:

sin A = sin (180 degrees - A)

Given that angle C = 35 degrees, we can solve for angle A:

180 degrees - A - C = 180 degrees
A = 180 degrees - 35 degrees
A = 145 degrees

Now we can substitute sin A and solve for b:

b = (15cm / sin 145 degrees) * sin (145 degrees)

Using a scientific calculator or an online sine calculator to evaluate sin 145 degrees is recommended.