In a triangle ABC two points D,E are taken on BC so that angle BAD=angle DAE=angleCAE. Determine AE if AB=5,BC=10 angle BAC=90.
1 answer:
Answer:
AE = 7.5
Step-by-step explanation:
Since <BAC = , then;
<BAD = <DAE = <CAE = (complementary angles)
From ΔABC, applying the Pythagoras theorem to determine the length of side AC;
=
+
=
+
100 = + 25
= 100 - 25
= 75
AC =
Applying trigonometric function to ΔCAE,
Cos =
AE = × Cos
= 7.5
Therefore, AE = 7.5
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Answer:
a
Step-by-step explanation:
A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.
Calculate slope m using the slope formula
m =
with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)
m = =
=
=
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= -
← slope of perpendicular bisector
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
(,
)
using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then
midpoint = ( ,
) = (
,
) = (1, 7 )
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - , then
y = - x + c ← is the partial equation
To find c substitute the midpoint (1, 7) into the partial equation
7 = - + c ⇒ c =
+
=
y = - x +
← equation of perpendicular bisector