Question

Which measurement of acute triangle ABC can you find by direct substitution of the labeled measures in the Law of Cosines?

picture: https://cdn.ple.platoweb.com/EdAssets/af030201291b4dff92556c977f88f313?ts=635296008180230000

answers are:
AC
m angle C
m angle A
none

Answer 1

example

Suppose a=56, b=97, c=112.
A = acos((b²+c²-a²)/(2bc)) = 29.99999986�
B = acos((c²+a²-b²)/(2ca)) = 60.00527405�
C = acos((a²+b²-c²)/(2ab)) = 89.99472609�

This is an amusing example, because it's a triangle that's almost a right triangle: a²+b²=12545, and c²=12544. In addition, this triangle has almost a 60� angle: c²+a²-b²=6271, and 2ca=6272. To find more examples of near 30-60-90 triangles, look for the continued fraction convergents to sqrt(3).

a is an element of A002530,
b is an element of A002531, and

Answer 2

c = 2a

Answer 3

do you know the Cosine Rule?

Answer 4

no

Answer 5

The cosine rule. We can use the cosine formula to find the length of a side or size of an angle. For a triangle with sides a,b and c and angles A, B and C the cosine rule can be written as: a2 = b2 + c2 - 2bc cos A.

Answer 6

Its applied when you know 2 sides and the included angle which is what we have he

Answer 7

* here

Answer 8

how do i calculate it?

Answer 9

the measurement you can find by using the Cosine rule is the side opposite the given angle.

Answer 10

what would i type in a calculator?

Answer 11

look at the formula in Supersmart's last post

plug in values b = 3 , c = 8 and A = 57.53

Answer 12

ok

Answer 13

is the answer m angle A?

Answer 14

No - the answer is a (in supersmart's post)

in this case a is the side opposite angle A - what side is this? Check the diagram.

Answer 15

1 sec

Answer 16

AC?

Answer 17

Yes , that's the correct choice.

Answer 18

thank you so much for the help

Answer 19

AC^2 = 3^2 + 8^2 - 2.3.8 cos 57.53

Answer 20

yw

Answer 21

oh i got it now thanks