Answer:
2.17ft/s
Step-by-step explanation:
Look at the sketch of ladder at the beginning and after 3 seconds it starts to fall,
Distance of ladder from the wall 3 seconds after ladder starts to fall = Initial distance+ Velocity× time
= 6 + 2×3
= 12ft
Use trignometry to find out the speed of the top of ladder
cosθ= 12/20
θ= 0.825 rad
tan θ= v/2
v= 2.17ft/s
Answer:
They are similar by the definition of similarity in terms of a dilation
Step-by-step explanation:
The given vertices of triangle ΔABC are;
A(1, 5), B(3, 9), and C(5, 3)
The vertices of triangle ΔDEF are;
D(-3, 3), E(-2, 5), and F(-1, 2)
Therefore, we get;
The length of segment, = √((9 - 5)² + (3 - 1)²) = 2·√5
The length of segment, = √((9 - 3)² + (3 - 5)²) = 2·√10
The length of segment, = √((5 - 3)² + (1 - 5)²) = 2·√5
The length of segment, = √((5 - 3)² + (-2 - (-3))²) = √5
The length of segment, = √((2 - 5)² + (-1 - (-2))²) = √10
The length of segment, = √((2 - 3)² + (-1 - (-3))²) = √5
∴ /
= 2·√5/(√5) = 2
/
= 2·√10/(√10) = 2
/
= 2·√5/(√5) = 2
The ratio of their corresponding sides are equal and therefore;
ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.