Question

In ΔABC, ∠C measures 46° and the values of a and c are 10 and 9, respectively. Find the remaining measurements of the triangle, and round your answers to the nearest tenth.

∠A = 82.2°, ∠B = 62.8°, b = 17.1
∠A = 53.1°, ∠B = 80.9°, b = 12.4
∠A = 53.1°, ∠B = 80.9°, b = 17.1
∠A = 82.2°, ∠B = 62.8°, b = 12.4

uwu plz help

Answer 1

@AZ

Answer 2

do you know how to do the sin, cos, tan stuff?

Answer 3

\(\color{#0cbb34}{\text{Originally Posted by}}\) @snowflake0531
do you know how to do the sin, cos, tan stuff?
\(\color{#0cbb34}{\text{End of Quote}}\)
No <3

Answer 4

ha, well, i can't explain that without confusing myself with the explanation lol
AZ is on

Answer 5

otay *patiently waits for az*

Answer 6

lollll
fine, welllll, i'll say that
sin(x) = opposite/hypotenuse
cos(x)=adjacent/hypotenuse
tan(x)=opposite/adjacent

Answer 7

We're not dealing with a 90 degree triangle so we have to use some other formulas.

Have you learned law of sine/law of cosine

Answer 8

yessir/ma'am/ fam I have learned that law :)

Answer 9

So we know 2 sides and 1 angle so far

We can use law of sine to find the angle opposite A

\(\dfrac{\sin A}{a} = \dfrac{\sin C}{c}\)

we know that a = 10
sin C = sin (46)
c = 9

so can you solve for A?

Answer 10

I think?

Answer 11

Let's put the numbers in

\(\dfrac{\sin A}{10} = \dfrac{\sin(46)}{9}\)

Use a calculator and can you tell me what sin(46) =

Answer 12

0.71933980033?

Answer 13

well, rounding it would be .72

Answer 14

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Kyky232
0.71933980033?
\(\color{#0cbb34}{\text{End of Quote}}\)

let's use all the digits we can for now

divide by 9 now

Answer 15

0.07992664448

Answer 16

now we have

\(\dfrac{\sin A}{10} = 0.07992664448\)

Multiply both sides by 10

Answer 17

SinA = 0.7992664448

Answer 18

Then we inverse Sine to get the angle of A

Answer 19

yeppi, correct

Answer 20

Exactly! So what is arcsin(0.7992664448)

Answer 21

what the heck is arcsin.... don't you just do sin^-1 ???

Answer 22

oh, just inverse lol

Answer 23

it would be 53.1 degrees

Answer 24

I know what arson is :)

Answer 25

sin^(-1) is the same as arcsin haha

Answer 26

nice

Answer 27

nice

Answer 28

this is geometry, you're in 10th grade?

Answer 29

8th :)

Answer 30

ha,, sameee

Answer 31

so yeah 53.1 degrees for A is correct

now we could first use law of cosines to find side B and then use law of sine to find angle b

but we're smarter than that. We know all the angles of a triangle add up to 180

so
53.1 + b + 46 = 180
angle b = ?

Answer 32

80.9 would be angle B

Answer 33

am big brain B)

Answer 34

now use law of sine again to calculate side B

\(\dfrac{\sin(46)}{9} = \dfrac{\sin(80.9)}{B}\)

Answer 35

now use law of sine again to calculate side B

\(\dfrac{\sin(46)}{9} = \dfrac{\sin(80.9)}{B}\)

Answer 36

lol, when she doesn't reply-

Answer 37

b = 12.4

Answer 38

Good job!