In geometry, it would be always helpful to draw a diagram to illustrate the given problem.
This will also help to identify solutions, or discover missing information.
A figure is drawn for right triangle ABC, right-angled at B.
The altitude is drawn from the right-angled vertex B to the hypotenuse AC, dividing AC into two segments of length x and 4x.
We will be using the first two of the three metric relations of right triangles.
(1) BC^2=CD*CA (similarly, AB^2=AD*AC)
(2) BD^2=CD*DA
(3) CB*BA = BD*AC
Part (A)
From relation (2), we know that
BD^2=CD*DA
substitute values
8^2=x*(4x) => 4x^2=64, x^2=16, x=4
so CD=4, DA=4*4=16 (and AC=16+4=20)
Part (B)
Using relation (1)
AB^2=AD*AC
again, substitute values
AB^2=16*20=320=8^2*5
=>
AB
=sqrt(8^2*5)
=8sqrt(5)
=17.89 (approximately)
Answer:
Approximately
.
Step-by-step explanation:
Convert the angle of this sector to radians:
.
The formula
relates the arc length
of a sector of angle
(in radians) to the radius
of this sector.
In this question, it is given that the arc length of this sector is
. It was found that
radians. Rearrange the equation
to find the radius
of this sector:
.
The perimeter of this sector would be:
.
Answer:
There is 1 solution.
Step-by-step explanation:
0.5(x - 3) = 3x - 2.5
0.5x - 1.5 = 3x - 2.5
-2.5x = -1
x = 0.4
There is 1 solution.
Answer:
y=-2
Step-by-step explanation:
you are solving for the variable y
add 3 to the opposite side, so it cancels out
y=-5+3
y=-2