The angles in a triangle are such that one angle is 120 degrees more than the smallest angle, while the third angle is 3 times a
1 answer:
Answer:
The measures of the angles are
,
and
Step-by-step explanation:
Let
x-----> one angle
y----> the smallest angle
z----> the third angle
we know that
-----> equation A
----> equation B
-----> equation C
substitute equation B and equation C in equation A and solve for y
<em>Find the measure of x</em>
<em>Find the measure of z</em>
therefore
The measures of the angles are ,
and
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Answer:
cos
(
5
π
12
)
=
√
2
−
√
3
2
Explanation:
By the half angle formula:
XXXX
cos
(
θ
2
)
=
±
√
1
+
cos
(
θ
)
2
If
θ
2
=
5
π
12
XXXX
then
θ
=
5
π
6
Note that
5
π
6
is a standard angle in quadrant 2 with a reference angle of
π
6
so
cos
(
5
π
6
)
=
−
cos
(
π
6
)
=
−
√
3
2
Therefore
XXXX
cos
(
5
π
12
)
=
±
⎷
1
−
√
3
2
2
XXXXXXXXXXX
=
±
⎷
2
−
√
3
2
2
XXXXXXXXXXX
=
±
√
2
−
√
3
4
XXXXXXXXXXX
=
±
√
2
−
√
3
2
Since
5
π
12
<
π
2
XXXX
5
π
12
is in quadrant 1
XXXX
→
cos
(
5
π
12
)
is positive
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XXXX
XXXX
(the negative solution is extraneous)
answer in pic more explain
