All categories

3 years ago

In a right triangle the leg opposite to the acute angle of 30° is 7 in. Find the hypotenuse and other leg.

Mathematics

2 answers:

fiasKO [112]3 years ago

8 0

Answer:

Hypotenuse = 14in

Adjacent = 12.12in

Step-by-step explanation:

Check attachment for diagram

Using SOH, CAH TOA method

According to SOH

Sin(theta) = Opposite/Hypotenuse

Given theta = 30°

Opposite = 7in

Sin30° = 7/Hypotenuse

Hypotenuse = 7/sin30°

Hypotenuse = 7/0.5

Hypotenuse = 14in

The other leg will be the adjacent say x

Using Pythagoras theorem to get x

Hyp² = Opp²+Adj²

14² = 7²+x²

x² = 14²-7²

x² = 196-49

x² = 147

x = √147

x = 12.12in

The value of the other leg is 12.12

Maksim231197 [3]3 years ago

5 0

This is a 30-60-90 triangle.
Therefore,
7 is A
the other leg is A√3
And the hypotenuse is 2A
So the other leg is 7√3 and the hypotenuse is 14

You might be interested in

Please please please help

weqwewe [10]

I believe it’s 80^, sorry if i’m wrong :)

8 0

2 years ago

Read 2 more answers

F(x)=2x+1/x-1 then f^-1(1)

olasank [31]

Answer:

f⁻¹(x) = (x + 1) / (x - 2)
f⁻¹(1 ) = - 2

Step-by-step explanation:

Given function:

f(x) = (2x + 1) / (x - 1)

Find its inverse, substitute x with y and f(x) with x, solve for y:

x = (2y + 1) / (y - 1)
x(y - 1) = 2y + 1
xy - x = 2y + 1
xy - 2y = x + 1
y(x - 2) = x + 1
y = (x + 1) / (x - 2)

Substitute y with f⁻¹(x):

f⁻¹(x) = (x + 1) / (x - 2)

Find f⁻¹(1 ):

f⁻¹(1 ) = ( 1 + 1) / (1 - 2) = 2 / - 1 = - 2

6 0

1 year ago

Help, these are yes or no answers.

djverab [1.8K]

Answer:

7:yes

8:no

9:yes

10:sorry

Step-by-step explanation:

3 0

2 years ago

THIS IS URGENT. A sign at the grocery store says that 3 cucumbers costs $3.60. How much would it cost for 5

Solnce55 [7]

Answer:

Step-by-step explanation:

just multiply

8 0

3 years ago

Read 2 more answers

Ye is riding home from a friend's house. After 5 minutes he is 4 miles from home, after 15 minutes Ye is 2 miles from home. Whic

Ad libitum [116K]

Answer:

$y = -\frac{1}{5}x + 5$

Step-by-step explanation:

Given

$5\ minutes = 4\ miles$

$15\ minutes = 2\ miles$

Required

Determine the equation

y represents distance

x represents time

So, the given parameters can be modeled (x,y) as:

$(x_1,y_1) = (5,4)$

$(x_2,y_2) = (15,2)$

First, we need to determine the slope of the function.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{2 - 4}{15 - 5}$

$m = \frac{-2}{10}$

$m = -\frac{1}{5}$

The equation can be determined using:

$y - y_1 = m(x - x_1)$

Where

$m = -\frac{1}{5}$

$(x_1,y_1) = (5,4)$

$y - y_1 = m(x - x_1)$

becomes

$y - 4 = \frac{-1}{5}(x - 5)$

Open bracket

$y - 4 = -\frac{1}{5}x + 1$

Solve for y

$y = -\frac{1}{5}x + 1 + 4$

$y = -\frac{1}{5}x + 5$

7 0

3 years ago