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2 years ago

5

AD is the angle bisector of ∠EAB. Solve for x. ANSWERS:

1 answer:

Fofino [41]2 years ago

7 0

Answer:

D) 6.4

Step-by-step explanation:

The Angle Bisector Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

This means that:

18/9.6 = 12/x

Solving for x:

x = 12*9.6/18

x = 6.4

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Learning goal: to understand the rules for computing dot products. let vectors a=(2,1,−4), b=(−3,0,1), and c=(−1,−1,2). part a -

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For this case we have the following vectors:
$a = (2,1, -4)

b = (- 3,0,1)

c = (- 1, -1,2)$
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3 years ago

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2 years ago

Mary is preparing for her birthday party , and she needs to give sweets to all her 10 friends who are invited . To do this , she

hram777 [196]

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2 years ago

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Nikitich [7]

Answer:

Area of trapezium = 4.4132 R²

Step-by-step explanation:

Given, MNPK is a trapezoid

MN = PK and ∠NMK = 65°

OT = R.

⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).

Now, sum of interior angles in a quadrilateral of 4 sides = 360°.

⇒ x + x + 65° + 65° = 360°

⇒ x = 115°.

Here, NS is a tangent to the circle and ∠NSO = 90°

consider triangle NOS;

line joining O and N bisects the angle ∠MNP

⇒ ∠ONS = $\frac{115}{2}$ = 57.5°

Now, tan(57.5°) = $\frac{OS}{SN}$

⇒ 1.5697 = $\frac{R}{SN}$

⇒ SN = 0.637 R

⇒ NP = 2×SN = 2× 0.637 R = 1.274 R

Now, draw a line parallel to ST from N to line MK

let the intersection point be Q.

⇒ NQ = 2R

Consider triangle NQM,

tan(∠NMQ) = $\frac{NQ}{QM}$

⇒ tan65° = $\frac{NQ}{QM}$

⇒ QM = $\frac{2R}{2.1445}$

QM = 0.9326 R .

⇒ MT = MQ + QT

= 0.9326 R + 0.637 R (as QT = SN)

⇒ MT = 1.5696 R

⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R

Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).

⇒ A = ( $\frac{NP + MK}{2}$ ) × (ST)

= ( $\frac{1.274 R + 3.1392 R}{2}$ ) × 2 R

= 4.4132 R²

⇒ Area of trapezium = 4.4132 R²

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