What is the numerator for the following rational expression?<br> e/f+8/f=?/f

Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC

Marysya12 [62]

BC is 10 units and AC is $5+5\sqrt{3}$ units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}$
AB is opposite to ∠C
BC is opposite to ∠A
AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ $\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

∵ AB = $5\sqrt{2}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}$

- By using cross multiplication

∴ (BC) × sin(30) = $5\sqrt{2}$ × sin(45)

∵ sin(30) = 0.5 and sin(45) = $\frac{1}{\sqrt{2}}$

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ $\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

- Substitute AB and the 3 angles in the rule above

∴ $\frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}$

- By using cross multiplication

∴ (AC) × sin(30) = $5\sqrt{2}$ × sin(105)

∵ sin(105) = $\frac{\sqrt{6}+\sqrt{2}}{4}$

∴ 0.5 (AC) = $\frac{5+5\sqrt{3}}{2}$

- Divide both sides by 0.5

∴ AC = $5+5\sqrt{3}$ units

BC is 10 units and AC is $5+5\sqrt{3}$ units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0

3 years ago

E. 2078-01-08

Mazyrski [523]

Answer:

the full question isn't there. what do you need to find the number of??

4 0

3 years ago

You buy a car for $25,000. It depreciates at the rate of 23% per year.

Juliette [100K]

The worth of the car in 10 years is $1,831.67 using an exponential equation approach.

What is an exponential equation?

An exponential equation is the one with exponents such X^3(the 3 is the exponent)

The exponential equation required here is the one where the future value would be lower than current value because the car reduces in value year-in-year-out.

FV=PV*(1-r)^N

FV=future worth of the car

PV=today's value=$25,000

r=depreciation rate=-23%

N=number of years=10

The fact that r is negative means the car is depreciating not appreciating.

FV=$25,000*(1-23%)^10

FV=$1,831.67

Find further explanation on exponential equation below in the link:

brainly.com/question/11832081

#SPJ1

7 0

2 years ago

A polygon has the following coordinates: A(3,1), B(5,3), C(2,5), D(-1,5), E(-4,3), F(-2,1). Find the length of DC.

nlexa [21]

To find the length of a line given two points, we are going to use the distance formula, which is defined below:

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

( $(x_1, y_1)$ and $(x_2, y_2)$ are the two points)

The points in this problem are (2, 5) and (-1, 5). We can find the distance of DC by substituting these values into the distance formula and simplifying, as shown below:

$D = \sqrt{(-1 - 2)^2 + (5 - 5)^2$