If a ramp makes an angle of 450 with the road and rises up to a height of 4 m, how long is the ramp?
Answers
Answer:
Solving Right Triangles
Key Questions
How do you find the missing angles when the sides of a right triangle are given?
In Triangle
A
B
C
with the right angle at
C
, let
a
,
b
, and
c
be the opposite, the adjacent, and the hypotenuse of
∠
A
. Then, we have
sin
A
=
a
c
⇒
m
∠
A
=
sin
−
1
(
a
c
)
sin
B
=
b
c
⇒
m
∠
B
=
sin
−
1
(
b
c
)
I hope that this was helpful.
Wataru · 1 · Oct 29 2014
How do you find all the missing angles, if you know one of the acute angles of a right triangle?
The sum of the measures of all the angles in a triangle is always equal to
180
o
.
In a right triangle, however, one of the angles is already known: the right angle, or the
90
o
angle.
Let the other two angles be
x
and
y
(which will be acute).
Applying these conditions, we can say that,
x
+
y
+
90
o
=
180
o
x
+
y
=
180
o
−
90
o
x
+
y
=
90
o
That is, the sum of the two acute angles in a right triangle is equal to
90
o
.
If we know one of these angles, we can easily substitute that value and find the missing one.
For example, if one of the angles in a right triangle is
25
o
, the other acute angle is given by:
25
o
+
y
=
90
o
y
=
90
o
−
25
o
y
=
65
o