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3 years ago

Points A, B, and C are collinear, and B lies between A and C. If AC = 48, AB = 2x+2, and BC = 3x+6, what is BC?

Mathematics

2 answers:

Vesna [10]3 years ago

8 0

Answer:

The value of BC is 30.

Step-by-step explanation:

Given information: A, B, and C are collinear, B lies between A and C, AC = 48, AB = 2x+2, and BC = 3x+6.

If A, B, and C are collinear, B lies between A and C, then by using segment addition property, we get

$AB+BC=AC$

Substitute AC = 48, AB = 2x+2, and BC = 3x+6 in the above equation.

$(2x+2)+(3x+6)=48$

On combining like terms we get

$(2x+3x)+(2+6)=48$

$5x+8=48$

Subtract 8 from both sides.

$5x=48-8$

$5x=40$

Divide 5 from both sides.

$x=8$

The value of x is 8.

We need to find the value of BC.

$BC=3x+6\Rightarrow 3(8)+6=30$

Therefore the value of BC is 30.

aleksandr82 [10.1K]3 years ago

4 0

Answer:

BC=30

Step-by-step explanation:

AC = 48

AB = 2x+2

BC=3x+6

AC= AB + BC

48 = 2x+2+3x+6

48=5x+8

5x=40

x=8

Hence

BC = 3(8)+6

BC=24+6

BC=30

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3 years ago

A helicopter is flying above a town. the local high school is directly to the east of the helicopter at a 20° angle of depressio

guapka [62]

Answer: 4.5 miles

Explanation:

When you draw the situation you find two triangles.

1) Triangle to the east of the helicopter

a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°

b) hypotensue = distance between the high school and the helicopter

c) opposite-leg to angle 20° = heigth of the helicopter

d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x

2) triangle to the west of the helicopter

a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°

b) distance between the helicopter and the elementary school = hypotenuse

c) opposite-leg to angle 62° = height of the helicopter

d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x

3) tangent ratios

a) triangle with the helicpoter and the high school

tan 20° = Height / x ⇒ height = x tan 20°

b) triangle with the helicopter and the elementary school

tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°

c) equal the height from both triangles:

x tan 20° = (5 - x) tan 62°

x tan 20° = 5 tan 62° - x tan 62°

x tan 20° + x tan 62° = 5 tan 62°

x (tan 20° + tan 62°) = 5 tan 62°

⇒ x = 5 tant 62° / ( tan 20° + tan 62°)

⇒ x = 4,19 miles

=> height = x tan 20° = 4,19 tan 20° = 1,525 miles

4) Calculate the hypotenuse of this triangle:

hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²

hipotenuse = 4.46 miles

Rounded to the nearest tenth = 4.5 miles

That is the distance between the helicopter and the high school.

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Step-by-step explanation:

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3 years ago

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