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maksim [4K]
3 years ago
7

Josh leans the ladder against a side of her house which is 10 feet. If the base of the latter is 3 feet away from the house, how

tall is the ladder? ( use Pythagorean theorem )
Mathematics
1 answer:
Galina-37 [17]3 years ago
4 0

Answer:

\sqrt{109}

Step-by-step explanation:

The side of the house is a side of the right triangle.

The ladder is 3 feet away, so it forms a triangle with sides 3, 10, x.

We're trying to find the hypotenuse, which is given by Pythagoras' Theorem:

a^2 + b^2 = c^2\\3^2 + 10^2 = x^2\\109 = x^2\\x = \sqrt{109}

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Given that sin theta = 1/4, 0
GaryK [48]
Answer: cos(Θ) = (√15) / 4

Explanation:

The question states:

1) sin(Θ) = 1/4

2) 0 < Θ < π / 2

3) find cos(Θ)

This is how you solve it.

1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).

(cos \alpha )^2 + (sin \alpha )^2 =1

2) From which you can find:

(cos \alpha )^2 = 1 - (sin \alpha )^2

3) Replace sin(α) with 1/4

=> (cos \alpha )^2 = 1 - (1/4)^2 = 1 - 1/16 = 15/16

=> cos \alpha =+/- \sqrt{15/16} = +/- (\sqrt{15} )/4

4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:

cos(Θ) = \sqrt{15} /4.

And that is the answer.
6 0
3 years ago
Q.23 Prove that: (sin4A - cos4A + 1) = 2sin2A
FrozenT [24]

Answer:

Step-by-step explanation:

I think you have the question incomplete, and that this is the complete question

sin^4a + cos^4a = 1 - 2sin^2a.cos^2a

To do this, we can start my mirroring the equation.

x² + y² = (x + y)² - 2xy,

This helps us break down the power from 4 to 2, so that we have

(sin²a)² + (cos²a)² = (sin²a + cos²a) ² - 2(sin²a) (cos²a)

Recall from identity that

Sin²Φ + cos²Φ = 1, so therefore

(sin²a)² + (cos²a)² = 1² - 2(sin²a) (cos²a)

On expanding the power and the brackets, we find that we have the equation proved.

sin^4a + cos^4a = 1 - 2sin^2a.cos^2a

4 0
3 years ago
Calculate the radius<br>22cm​
sweet [91]

Answer:

11

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please help me......
MrMuchimi

Answer:

it's answer is 107

Step-by-step explanation:

firstly

x+28+45=180

x+73=180

x=180 subtract 73 = 107

5 0
3 years ago
Read 2 more answers
Can three line segments with the given lengths form a right triangle?
musickatia [10]

Answer:

Yes

12, 35, 37

16, 30, 34

20, 21, 29

No

18, 24, 42

Step-by-step explanation:

Required

Determine which length form a right triangle

To do this, we make use of Pythagoras theorem where the square of the largest length = the sum of the squares of the other lengths

So:

(1) 12, 35, 37 --- Yes

37^2 = 35^2 + 12^2

1369 = 1225 + 144

1369 = 1369

(2) 16, 30, 34 --- Yes

34^2 = 16^2 + 30^2

1156 = 256 + 900

1156 = 1156

(3) 18, 24, 42 --- No

42^2 =18^2 + 24^2

1764 =324 + 576

1764 =900

1764 \ne 900

(4) 20, 21, 29 -- Yes

29^2 = 20^2 + 21^2

841= 400 + 441

841= 841

3 0
2 years ago
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