All categories

3 years ago

In the following triangle,what is the length of the hypotenuse?

Mathematics

2 answers:

kati45 [8]3 years ago

4 0

Step-by-step explanation:

using trigonometric ratios,

sin theta= opposite ÷ hypoteneus (h)

sin 45°= 3 root 2 ÷ h

1/root 2= 3 root 2 ÷h

h= 3× root 2 × root 2

= 3×2

= 6 unit

lesantik [10]3 years ago

4 0

Answer:

Step-by-step explanation:

The given triangle is a right angle triangle and also an isosceles triangle.

The hypotenuse is the longest side of the right angle triangle. To determine the hypotenuse, we will apply trigonometric ratio

Sin θ = opposite side/hypotenuse

Looking at the triangle.

θ = 45 degrees = 1/√2

opposite side = 3√2

Therefore,

Sin 45 = 3√2/hypotenuse

1/√2 = 3√2/hypotenuse

hypotenuse × 1 = √2 × 3√2

hypotenuse = 3√2 × √2

hypotenuse = 3 × 2 = 6

Alternatively,

We can apply Pythagoras theorem since both sides are equal

Since the length of one side is 3√2, then the length of the other side is also 3√2

Hypotenuse^2 = opposite side^2 + adjacent side^2

Hypotenuse^2 = (3√2)^2 + (3√2)^2

Hypotenuse^2 = 18 + 18 = 36

Hypotenuse = √36 = 6

You might be interested in

Help somebody thanks .

Fudgin [204]

It’s going to be 6 units

7 0

2 years ago

For x > 3, values of the function f(x) = –(x – 3)^2(x + 2) are negative. On this same interval, which statement correctly des

Andrej [43]

For x > 3, values of the function f(x) = –(x – 3)2(x + 2) are negative. On this same interval, which statement correctly describes the values of the additive and multiplicative inverses?

4 0

2 years ago

Read 2 more answers

The U.S. and many other countries have recently tightened airport security. A sociologist is interested in estimating the propor

melisa1 [442]

Answer:

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

Step-by-step explanation:

Conduct a test to determine whether the true proportion of interest is higher than 0.7.

This means that the null hypothesis is: $H_{0}: p = 0.7$

And the alternate hypothesis is: $H_{a}: p > 0.7$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that $\mu = 0.7, \sigma = \sqrt{0.7*0.3}$

The sociologist found that 375 of the 500 travelers randomly selected and interviewed indicated that the airports were safe.

This means that $n = 500, X = \frac{375}{500} = 0.75$

Value of the z-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.75 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{350}}}$

$z = 2.44$

P-value of the test:

Probability of z being larger than 2.44, that is, a proportion larger than 0.75.

This is, looking at the z-table, 1 subtracted by the pvalue of Z = 2.44. S

Z = 2.44 has a pvalue of 0.9927

1 - 0.9927 = 0.0073

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

8 0

3 years ago

Fill in the blanks:

muminat

6x + y = 1 , y, y, -6x + 1 or 1 - 6x

7 0

3 years ago

The price of a video game is $35.60. If you purchase the video game for $30.26 with a coupon, what percent of the original price

topjm [15]

(30.26/35.6)*100= 85%

check: .85 * 35.6 = 30.26

4 0

3 years ago