Find the area of ΔABC.

Mathematics

1 answer:

zysi [14]3 years ago

6 0

Answer:

Step-by-step explanation:

You know two sides of the triangle and the angle between them, so use the Law of Cosines to solve the triangle.

a² = √(b²+c² - 2bc·cosA)

= √(9²+7.8² - 2·9·7.8·cos(32°)

≅ 4.8

Then use Heron's formula to calculate the area.

semiperimeter s = 0.5×(a+b+c) ≅ 10.8

area = √(s-(s-a)(s-b)(s-c)) ≅ 18.6 square units

You might be interested in

The mean of this data is 8 what two numbers could go in the blanks <br><br> 12,4,9,13,7,11,5,2,-,-

Sophie [7]

12+4+9+13+7+11+5+2+_+_ /10= 8
x10 both sides

12+4+9+13+7+11+5+2+_+_=80
63+_+_=80
-63 both sides
_+_= 17
any two numbers that add up to 17 can go in the planks
7,10

4 0

4 years ago

lisov135 [29]

Answer:

it is answer 3/4

Step-by-step explanation:

6 0

3 years ago

The period T (in seconds) of a pendulum is given by T=2\pi \sqrt((L)/(32)), where L stands for the length (in feet) of the pendu

Vsevolod [243]

The first thing we must do in this case is to rewrite the equation correctly:
T = 2 * pi * root (l / 32)
From here, we clear l:
T / (2 * pi) = root (l / 32)
l / 32 = (T / (2 * pi)) ^ 2
l = 32 * (T / (2 * pi)) ^ 2
Substituting values:
l = 32 * (1.57 / (2 * 3.14)) ^ 2
l = 2 feet
Answer:
the length is:
l = 2 feet

7 0

3 years ago

12. The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each.

Debora [2.8K]

Answer:

The number of tickets they have sold in advance are summed up with the following equation and solution:

Equation: $\frac{6842.50}{17.50}$ [the final answer should be in dollars]

Solution: The Opera sold 391 tickets in advance.

Step-by-step explanation:

First: Review some background information:

Let's see what the problem gives us to answer it. I'll bold out the important parts:

The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each. If they have collected $6842.50 already, then how many tickets have they sold in advance?

We know how much the tickets cost and how much money they have earned from selling tickets, we can find out how much tickets they have sold.

Second: Solve the problem:

We can solve this problem using many ways, but I'm just going to pick one. We will use proportions to answer this. Now thoughts might be going through your head like this: What is this guy saying? What in the world is proportions? Well hopefully you learn from this example (Please don't take offense if you <em>do</em> know how to do proportions).

First we set up two fractions. One ticket costs $17.50, so we will use it to set up our first fraction: $\frac{1}{17.50}$ . We don't know how many tickets all together cost $6842.50 so we will use the variable: x. Now, we can set up our second fraction. x tickets costs $6842.50 so our second fraction will be: $\frac{x}{6842.50}$ . Now we must use cross multiplication. We multiply the numerator of the first fraction times the denominator of the second fraction, and then we multiply the denominator o the first fraction times the numerator of the second fraction. That's what we would do usually. But now, since we have a variable, we must use cross multiplication to solve for this variable. So we multiply the the numerator of the first fraction times the denominator of the other fraction and then we divide that answer times the denominator of the first fraction (You don't have to set it up like this).So let's solve this question: