Which one is bigger, 6200 ft or 1 mi and 900 feet

QveST [7]

The answer to this equation would be 3.

7 0

3 years ago

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

Theo bought 2 hot dogs and two drinks for $4.00. At the same concession stand, Vicky bought 3 hot dogs and a drink for $4.50. Wr

Sedbober [7]

Answer:

The hot dog are $2.63

Step-by-step explanation:

Hot Dogs = H

Drinks = D

2H + 2D = 4

Divide both sides by 2

H + D = 2

Subtract D from either side

H = 2 -D

3H + D = 4.50

Plug in 2 - D for H

3(2- D ) + D = 4.50

6 - 3D + D = 4.50

6 - 4D = 4.50

Add 6 to either side

-4D = 10.50

Divide either side by -4

D = -2 . 625

3 0

2 years ago

The diagram shows a right-angled triangle.

Margarita [4]

1/sin(38)*7=11.4
Hope it helps

6 0

2 years ago

6. Find the value of r in the following triangle.

makkiz [27]

Answer:

r = 19.2deg

Step-by-step explanation:

6r + 5 = 30 + 90 (exterior angles of a triangle)

6r = 115

r = 19.2deg (1dp)

Topic: Angles

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

3 0

2 years ago