2. The side of a parallelogram is 2 tii
what is the area of the parallelogra
3. If one angle of a right angle triangle
4. Find the value of a : 28/56 = 4/a
5. Express the following in standard for
6. Give reason and is it possible to drau
Answers
Step-by-step explanation:
We can drop a perpendicular from
C
to the x-axis (this is the altitude or height). Recalling the basic trigonometric identities, we know that
c
o
s
θ
=
x
(adjacent)
b
(hypotenuse)
and
s
i
n
θ
=
y
(opposite)
b
(hypotenuse)
In terms of
θ
,
x
=
b
c
o
s
θ
and
y
=
b
s
i
n
θ
.
The
(
x
,
y
)
point located at
C
has coordinates
(
b
c
o
s
θ
,
b
s
i
n
θ
)
.
Using the side
(
x
−
c
)
as one leg of a right triangle and
y
as the second leg, we can find the length of hypotenuse
a
using the Pythagorean Theorem. Thus,
a
2
=
(
x
−
c
)
2
+
y
2
=
(
b
c
o
s
θ
−
c
)
2
+
(
b
s
i
n
θ
)
2
Substitute
(
b
c
o
s
θ
)
for
x
and
(
b
s
i
n
θ
)
for
y
.
=
(
b
2
c
o
s
2
θ
−
2
b
c
c
o
s
θ
+
c
2
)
+
b
2
s
i
n
2
θ
Expand the perfect square
.
=
b
2
c
o
s
2
θ
+
b
2
s
i
n
2
θ
+
c
2
−
2
b
c
c
o
s
θ
Group terms noting that
c
o
s
2
θ
+
s
i
n
2
θ
=
1.
=
b
2
(
c
o
s
2
θ
+
s
i
n
2
θ
)
+
c
2
−
2
b
c
c
o
s
θ
Factor out
b
2
.
a
2
=
b
2
+
c
2
−
2
b
c
c
o
s
θ
The formula derived is one of the three equations of the Law of Cosines. The other equations are found in a similar fashion.
Keep in mind that it is always helpful to sketch the triangle when solving for angles or sides. In a real-world scenario, try to draw a diagram of the situation. As more information emerges, the diagram may have to be altered. Make those alterations to the diagram and, in the end, the problem will be easier to solve.
HOPE IT HELPS