As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.
The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the
trusty calculator:
B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !
Answer:
7 and 9 are alternate interior angles
Step-by-step explanation:
4 and 11 are corresponding angles
1 and 7 are vertical angles
Answer:
500
Step-by-step explanation:
Well you find one tenth of a number by dividing it by 10
So to do the opposite, you can do 50*10 which is 500
Or if you really wanted to you could go through each option dividing them all by 10 till you got 50
9
yea........ hi how you doinn
Answer:
2 - 
Step-by-step explanation:
Using the addition formula for tangent
tan(A - B) =
and the exact values
tan45° = 1 , tan60° =
, then
tan15° = tan(60 - 45)°
tan(60 - 45)°
= 
=
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
The conjugate of 1 +
is 1 -
=
← expand numerator/denominator using FOIL
= 
= 
=
+ 
= 2 - 