Question

To prepare for a triathlon, Amanda starts from position A and rides her bike along a straight road for 12 miles to reach position B. At B, she turns left and rides along another straight road for 15 miles to reach position C. At C, she turns left again and rides 20 miles along a straight road to return to A. In ΔABC, what are m∠A, m∠B, and m∠C, respectively?

Answer 1

@ranga @RosieF @robtobey

Answer 2

@Johnbc

Answer 3

Do you know the trigonometric functions for angles and sides of the angles?

Answer 4

sines and cosines?

Answer 5

Yup

Answer 6

Do you know the sides that Sine, Cosine, and tangent relate to?

Answer 7

not really..

Answer 8

i know the formulas for sines and cosines

Answer 9

What are they?

Answer 10

for sines:\[\frac{ SinA }{ a }=\frac{ SinB }{ b }=\frac{ SinC }{ c }\]

Answer 11

Cosines:\[a^2=b^2+c^2-2bc*\cos(A)\]

Answer 12

\[b^2=a^2+c^2-2ac*\cos(B)\]

Answer 13

\[c^2=a^2+b^2-2ab*\cos(C)\]

Answer 14

those are the formulas

Answer 15

Those are definitely the formulas but there are easier forms for angles

Answer 16

there is?

Answer 17

okay

Answer 18

im looking for all 3 angles

Answer 19

Yup

Answer 20

And depending on the angle that you want to find first you can use the corresponding formula

Answer 21

okay so its CAH. Adjacent and Hypotenuse

Answer 22

This is NOT a right triangle.

Answer 23

Use the Law of Cosines to find angle A.

a^2 = b^2 + c^2 - 2bc * cos(A)
15^2 = 20^2 + 12^2 - (2)(20)(12)cos(A).
Solve for angle A.

Then you can use the Law of Sines to find angle B
a / sin(A) = b / sin(B).

Then you can find angle C as 180 - angle A - angle B

Answer 24

im not doing something right, i got 0.84

Answer 25

15^2 = 20^2 + 12^2 - (2)(20)(12)cos(A).
225 = 400 + 144 - 480cos(A)
480cos(A) = 400 + 144 - 225 = 319
cos(A) = 319/480 = 0.6645833
A = arccos(0.664583) = 48.35 degrees.

Answer 26

okay so m<A= 48.35degress

Answer 27

Find angle B using the Law of Sines.

Answer 28

94.94 degrees

Answer 29

I have not done the calculation but I will have to assume you did it correctly.

Answer 30

Yes, 94.94 degrees is correct.

Answer 31

the other angle is 36.71

Answer 32

Yes.
Not sure at what decimal place they want you to round off the angles.

Answer 33

2

Answer 34

okay, then you have the answer.

Answer 35

okay thank you so much

Answer 36

You are welcome.

Answer 37

the answer is 48.35°, 94.94°, 36.71°