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vodomira [7]
3 years ago
8

Given: ∆ABC, m∠C = 90° m∠BAC = 2m∠ABC BC = 24, AL −∠ bisector Find: AL

Mathematics
1 answer:
emmasim [6.3K]3 years ago
6 0
The answer is that AL is equal to 16.

Given that in triangle ABC, m∠C=90,
it means m∠A +∠B= m∠BAC + m∠ABC = 90
m∠ABC = 90 - m∠BAC
Also given that;m∠BAC = 2m∠ABC
So,
m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC
m∠BAC +2m∠BAC = 180
3m∠BAC = 180
m∠BAC=180/3 = 60
m∠ABC = 60/3 = 30
thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,
AC=24/√3=8√3AL bisects angle A =>m∠LAC=30
ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16
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I think best word to insert in the blank is the term "bisecting".

An altitude of a triangle is a line or segment that passes through a vertex of the triangle and is bisecting <span>to the line containing the opposite side.

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3 years ago
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1. what is the perimeter of the triangle?<br> 2. what is the area of the triangle?
jonny [76]

Answer:

See below. A=45 p=39.64

Step-by-step explanation:

Hi = 9 squares (h)

Gh= 14 squares. (b)

Area of a triangle = 1/2 bxh

1/2 14 x 9

7x9= 45.

Area =45 squares.

Perimiter

A= side hi (9)

B= side gh (14)

C= side gi (unknown)

A^2 + b^2 = c^2

9^2 + 14^2 = 277

C^2 = 277

Square root of 277 =c

C length =16.64 squares

A+b+c = perimeter

9+14+16.64 = 39.64 squares.

Sorry I cannot see the units of measure in the photo

7 0
3 years ago
NEED HELP IN FIVE MINUTE PLZ HURRY
Y_Kistochka [10]

Answer:

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Step-by-step explanation:

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Which equation in slope intercept represents the line that goes through the points (-1, 6) and (1, -2)
Afina-wow [57]

Answer:

D) y=-4x+2

Step-by-step explanation:

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

m=(-2-6)/(1-(-1))

m=-8/(1+1)

m=-8/2

m=-4

y-y1=m(x-x1)

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y-6=-4(x+1)

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) Final averages are typically normally distributed with a mean of 72 and a standard deviation of 12.5. Your professor states th
Bad White [126]

Answer:

65.45

Step-by-step explanation:

Zscore = (x - mean) / standard deviation

x = score

Percentage below C :

D = 18% ; F = 12%

Sum = 30%

Obtain the Zscore for the proportion below D

P(Z < 0.30) = -0.524

Hence, Zscore = -0.524

Put Zscore = -0.524 in the equation :

-0.524 = (x - 72) / 12.5

-0.524 * 12.5 = x - 72

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-6.55 + 72 = x

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