The age of a car and the value of the car<br> O Positive Correlation<br> O Negative correlation

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

2 years ago

Jenny earned a 77 on her most recent test. Jenny’s score is no less than 5 points greater than Four-fifths of Terrance’s score.

Nina [5.8K]

Answer:

Its A

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Please answer do not answer if u don't know the answer

Hitman42 [59]

Answer :x=3 y=7 (3,7)

Step-by-step explanation: I took algebra last year and I answered your question earlier.

4 0

2 years ago

The area of the square is 100 square centimeters. What is the area of the circle?

swat32

Answer:

Since the question is incomplete, see the figure attached and the explanation below.

Explanation:

Since the figure is missing, I enclose the figure of a square inscribed in a circle.

Since the <em>area of a square</em> is the side length squared, you can determine the side length:

Area = (side length)²

100 cm² = (side lenght)²

$side\text{ }length=\sqrt{100cm^2}=10cm$

From the side length, you can find the diagonal of the square, which is equal to the diameter of the circle, using the Pythagorean theorem:

diagonal² = (10cm)² + (10cm)² = 2 × (10cm)²

$diagonal=\sqrt{2\times (10cm)^2}\\ \\ diagonal=10\sqrt{2} cm$

The area of the circle is π (radius)².

radius = diameter/2 = diagonal/2

$area= \pi \times (5\sqrt{2}cm)^2=50\pi cm^2$

6 0

2 years ago

The original cost of a pair of shoes is 850dhs. The store offers a markup of 30%. Find the retail price of pair of shoes.

mamaluj [8]

Answer:

Step-by-step explanation:

7 0

2 years ago

The age of a car and the value of the car O Positive Correlation O Negative correlation