Whats the length in the picture

Suppose we have a right triangle with legs of length a and b and hypotenuse of length c. Suppose b=3 and c=5. Then a= , For the

ANTONII [103]

Answer:

Length of right-angle triangle 'a' = 4

b)

$sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}$

$cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}$

$tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}$

Step-by-step explanation:

Step(i):-

Given b = 3 and hypotenuse c = 5

Given ΔABC is a right angle triangle

By using pythagoras theorem

c² = a² + b²

⇒ a² = c² - b²

⇒ a² = 5²-3²

=25 - 9

a² = 16

⇒ a = √16 = 4

The sides of right angle triangle a = 4 ,b = 3 and c = 5

Step(ii):-

$sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}$

$cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}$

$tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}$

7 0

3 years ago

Three consecutive terms of an arithmetic sequence have a sum of 12 and a product of -80. Find the terms. Hint: let the terms be

Shalnov [3]

(x - d) + x + (x + d) = 12 --> Create an equation using the first piece of information - "Three consecutive terms... have a sum of 12"

x - d + x + x + d = 12 --> Simplify the left side of this equation (d cancels out)

3x = 12 --> Divide both sides by 3

x = 4


Use the value of x (x = 4) to find the value of d. To do this, set up another equation using the second piece of information.

(x - d) * (x + d) * x = - 80 --> "Three consecutive terms... have... a product of -80". Then, substitute the value of x (4) into this equation.

(4 - d) * (4 + d) * 4 = - 80 --> Multiply out the sets of brackets, the * 4 is dealt with afterwards

4(16 - 4d + 4d - d²) = - 80 --> Simplify the expression inside the brackets

4(16 - d²) = - 80 --> Multiply out these brackets by the 4

64 - 4d² = - 80 --> Subtract 64 from both sides

- 4d² = - 144 --> Divide both sides by - 4

d² = 36 --> Square root both sides

d = 6

Now, find the values of the terms of the sequence by using substituting the values of x and d into the expressions given.

1. x - d = 4 - 6 = - 2
2. x = 4
3. x + d = 4 + 6 = 10

The three terms are - 2, 4, 10.

5 0

3 years ago

Which two expressions are equivalent to 24m-12p+72?

zubka84 [21]

Option 3 is the correct answer

3 0

4 years ago

HELP PLZZ !

lorasvet [3.4K]

Answer: A, C, and D

Step-by-step explanation:

3 0

3 years ago

Cindy works at Jurassic Park and has been tasked to design a container in the shape of a

vichka [17]

The amount Cindy should increase for each dimension of the scaled model will be 12 meters.

<h3>What is the scale factor?</h3>

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Given that:-

The scaled model of the container has dimensions of 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model.

The scale model will be solved as follows:-

Present volume = 2 x 4 x 6 = 48 cubic meters

Let the lengths be increased by x meters now the new volume will be:-

( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84

( x² + 6x + 8 ) ( 6 + x ) = 48 x 84

( x³ + 44x + 12x² - 3984 ) = 0

By solving the cubic equation we will get the value of x = 12 meters.

Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.

To know more about scale factors follow

brainly.com/question/25722260

#SPJ1

8 0

3 years ago