When you flip a biased coin the probability of getting a tail is 0.41.

Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C o

Brrunno [24]

Answer:

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

$Sin\ C = \frac{h}{a}$

Make h the subject:

$h = aSin\ C$

Also, in BOC (Using Pythagoras)

$a^2 = h^2 + x^2$

Make $x^2$ the subject

$x^2 = a^2 - h^2$

Substitute $aSin\ C$ for h

$x^2 = a^2 - h^2$ becomes

$x^2 = a^2 - (aSin\ C)^2$

$x^2 = a^2 - a^2Sin^2\ C$

Factorize

$x^2 = a^2 (1 - Sin^2\ C)$

In trigonometry:

$Cos^2C = 1-Sin^2C$

So, we have that:

$x^2 = a^2 Cos^2\ C$

Take square roots of both sides

$x= aCos\ C$

In triangle BOA, applying Pythagoras theorem, we have that:

$AB^2 = h^2 + (b-x)^2$

Open bracket

$AB^2 = h^2 + b^2-2bx+x^2$

Substitute $x= aCos\ C$ and $h = aSin\ C$ in $AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2$

Open Bracket

$AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C$

Reorder

$AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C$

Factorize:

$AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C$

In trigonometry:

$Sin^2C + Cos^2 = 1$

So, we have that:

$AB^2 = a^2 * 1 + b^2-2abCos\ C$

$AB^2 = a^2 + b^2-2abCos\ C$

Take square roots of both sides

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

6 0

3 years ago

7. All quadrilaterals have 4 sides and a trapezoid is a quadrilateral. How many sides does a trapezoid have? A: 5 B: 4 C: 3 D: 2

nata0808 [166]

Answer:

B: 4

Step-by-step explanation:

A trapezoid have 4 sides.

Hope it helps you in your learning process

5 0

2 years ago

Read 2 more answers

What is the equation parallel to 4y-3x=8

Andreyy89

Answer:

Whatever option has a slope of 3/4 and isn't y = 3/4x + 2

Step-by-step explanation:

This means that it has to have a slope of 3/4 (written as 3/4x + b). This is because parallel lines have the same slope; rearranging the first equation gets us y = 3/4x + 2. So, our slope for a parallel line has to be 3/4.

6 0

3 years ago

Mike scored a 125 at a semi-final dividing competition season. He scored 95 at this final season. What is the percentage decreas

IrinaK [193]

Answer:

There was a 24% decrease

Step-by-step explanation:

Percentage decrease = (final season's score - semi-final score) / semi final score x 100

$\frac{95-125}{125}$ ×100

$\frac{-30}{125}$ × 100 = -24%

3 0

2 years ago

Jess wants 180 cupcakes for her party. Jess has already made 60 berry cupcakes, and 48

Pavel [41]

Answer:

Hi! The answer to your question is 72 Cupcakes

Step-by-step explanation:

$60+48 = 108$

$180 - 108 = 72$

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☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

5 0

2 years ago