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gizmo_the_mogwai [7]
2 years ago
11

13. In A ABC, if m BF is an angle bisector, find m

Mathematics
1 answer:
Tresset [83]2 years ago
4 0

If in the triangle ABC , BF is an angle bisector and ∠ABF=41° then angle m∠BCE=8°.

Given that m∠ABF=41° and BF is an angle bisector.

We are required to find the angle m∠BCE if BF is an angle bisector.

Angle bisector basically divides an angle into two parts.

If BF is an angle bisector then ∠ABF=∠FBC by assuming that the angle is divided into two parts.

In this way ∠ABC=2*∠ABF

∠ABC=2*41

=82°

In ΔECB we got that ∠CEB=90° and ∠ABC=82° and we have to find ∠BCE.

∠BCE+∠CEB+EBC=180  (Sum of all the angles in a triangle is 180°)

∠BCE+90+82=180

∠BCE=180-172

∠BCE=8°

Hence if BF is an angle bisector then angle m∠BCE=8°.

Learn more about angles at brainly.com/question/25716982

#SPJ1

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Answer:

65m^5n³

Step-by-step explanation:

(13m³n¹)(5m²n²)

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8 0
3 years ago
A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 49.
Kobotan [32]

Answer:

The numbers are

-2+3\sqrt{5}   and 3\sqrt{5}

Step-by-step explanation:

Let

x -----> the smaller positive real number

y -----> the larger positive real number

we know that

A positive real number is 2 less than another

so

x=y-2

y=x+2 ----> equation A

When 4 times the larger is added to the square of the smaller, the result is 49

so

4y+x^2=49 ----> equation B

substitute equation A in equation B

4(x+2)+x^2=49

solve for x

x^2+4x-41=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^2+4x-41=0

so

a=1\\b=4\\c=-41

substitute in the formula

x=\frac{-4\pm\sqrt{4^{2}-4(1)(-41)}} {2(1)}

x=\frac{-4\pm\sqrt{180}} {2}

x=\frac{-4\pm6\sqrt{5}} {2}

x=-2\pm3\sqrt{5}

so

The positive real number is

x=-2+3\sqrt{5}

Find the value of y

y=x+2

y=-2+3\sqrt{5}+2

y=3\sqrt{5}

6 0
4 years ago
HELP DUE IN 10 MINS! Use right triangle trig to solve for the missing angles. Round all answers to the nearest degree (whole num
pogonyaev

Answer:

relationship between base and perpendicular is given by tan angle

tan ?=perpendicular./base

tan?=5/16

?=tan-¹(5/16)=17.35=17

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3 years ago
What is the scale factor from triangle ABC to triangle GHI
Len [333]

Answer:

4

Step-by-step explanation:

8 0
3 years ago
Find the x- and y- intercepts if the line that passes through the given points (-6,-6),(4,-2).
Paul [167]

Answer:

The x-intercept would be 9 and the y-intercept would be -18/5

Step-by-step explanation:

In order to find this we need to first find the slope. To do that we use the two points and the slope equation.

m (slope) = (y2 - y1)/(x2 - x1)

m = (-2 - -6)/(4 - -6)

m = 4/10

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Now that we have the slope, we can use that and either point to find the equation of the line in standard form.

y - y1 = m(x - x1)

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-2/5x + y = -18/5

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Now that we have this, we can find the intercepts through using 0s. First, we put a zero in for y to find the x intercept.

-2x + 5y = -18

-2x + 5(0) = -18

-2x = -18

x = 9

Therefore the x intercept is 9.

We find the y-intercept by doing the opposite. We put a 0 in for x.

-2x + 5y = -18

-2(0) + 5y = -18

5y = -18

y = -18/5

5 0
3 years ago
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