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4 years ago

Find the measure of each side of angle abc with vertices a(-1,5) b(6,1) and c(2,-6)

Mathematics

1 answer:

Alex17521 [72]4 years ago

5 0

Answer:

√65,√65 and √129

Step-by-step explanation:

To find the measure of each side of a triangle, we use the distance formula to get it.

The distance Formula is given as:

Distance between two points = √[x2-x1]² + [y2-y1]²

A= (-1, 5), B=(6,1), C=(2,-6)

Going by the distance formula:

Distance AB is given as:

AB= √[6-(-1)]² + [1-5]²

AB= √49 + 16 = √65

Distance BC is given as:

BC= √[2-6]² + [-6-1]²

BC= √16 + 49 = √65

Distance AC ia given as:

AC= √[2-(-1)]² + [-6-5]²

AC= √3² + 11² = √129

Since two sides are equal, the triangle in question is an isosceles triangle.

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Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tent

nalin [4]

Answer:

The last one $(x=11.3, y=8)$ .

Step-by-step explanation:

1) There are three trigonometric ratios for right-angled triangles.

$sin()=\frac{opposite}{hypotenuse}\\cos()=\frac{adjacent}{hypotenuse}\\tan()=\frac{opposite}{adjacent}$

In a right triangle, the hypotenuse, h, is the side opposite the right angle. Relative to the acute angle θ, check the attachment, the legs are called the opposite side, o, and the adjacent side a.

2) In this case, we are given a length and an angle to find x and y.

Let's find x first. To find x we need to use $sin()=\frac{opposite}{hypotenuse}$ .

$sin(45)=\frac{8}{x}\\sin(45)x=8\\x=\frac{8}{sin(45)} \\x=11.31$

Find y.

Notice that, we can use the Pythagorean Theorem $(c^2=a^2+b^2)$ to find y.

$c^2=a^2+b^2$

$11.31^2=8^2+b^2\\11.31^2 - 8^2 = b^2\\63.9161 = b^2\\\sqrt{63.9161} = b\\b = 7.99$

3) Round them off to the nearest tenth.

$x=11.31\\x=11.3$

$y=7.99\\y=8$

Therefore, the correct choice is the last one $(x=11.3, y=8)$ .

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2 years ago

Which of the following expression does not include a variable

lesya [120]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

563,626 nearest hundred thousand

chubhunter [2.5K]

That answer would be 600,000 I think

4 0

3 years ago

What is the value of this expression when la=7 and b= 4? |2a|-b/3

KiRa [710]

Answer:

12.666 is the answer

Step-by-step explanation:

2*7-4/3

14-4/3

42/3-4/3

38/3=12.666

7 0

3 years ago

A spice store charges $2.75 for 25 grams of paprika. It also charges 5% of the purchase price for shipping any order

Whitepunk [10]

Answer:

Part a) The expression is $3.2445x$

Part b) Customer cannot buy 2.5 ounces of paprika and have it shipped for less than $8.00

Step-by-step explanation:

The complete question is

A spice store charged 2.75 for 25 grams of paprika. It also charges 5% of the purchase price for shipping any order.

Part a) Write and simplify an expression to determine the cost of buying and shipping x ounces of paprika. Use 1 ounce = 28 grams

Part b) Can a customer buy 2.5 ounces of paprika and have it shipped for less than 8.00? Explain

step 1

Convert grams to ounces

Remember that

$1\ oz=28\ g$

To convert grams to ounces divide by 28

$25\ g=25/28= 0.89\ oz$

The unit price is

$2.75/0.89=3.09\frac{\$}{oz}$

Let

x ----> the number of ounces of paprika

y ----> the cost of buying and shipping x ounces of paprika

5%=5/100=0.05

$y=3.09x+(3.09x)0.05\\y=3.09x[1+0.05]\\y=3.2445x$

Part b) For x=2.5 oz

substitute in the equation

$y=3.2445(2.5)=\$8.11$

$\$8.11 > \$8.00$

therefore

Customer cannot buy 2.5 ounces of paprika and have it shipped for less than $8.00

6 0

3 years ago

Find the measure of each side of angle abc with vertices a(-1,5) b(6,1) and c(2,-6)​

Find the measure of each side of angle abc with vertices a(-1,5) b(6,1) and c(2,-6)