A kite with a 100 foot-long string is caught in a tree. When the full length of the string is stretched in a straight line to the ground, it touches the ground a distance of 30 feet from the bottom of the tree. Find the measure of the angle between the kite string and the ground.

17°

27°

63°

73°

Step-by-step explanation:

3 0

3 years ago

given that sin theta= 1/4, 0 is less than theta but less than pi/2, what is the exact value of cos theta

lapo4ka [179]

Answer:

$\cos{\theta} = \frac{\sqrt{15}}{4}$

Step-by-step explanation:

For any angle $\theta$ , we have that:

$(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1$

Quadrant:

$0 \leq \theta \leq \frac{\pi}{2}$ means that $\theta$ is in the first quadrant. This means that both the sine and the cosine have positive values.

Find the cosine:

$(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1$

$(\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1$

$\frac{1}{16} + (\cos{\theta})^{2} = 1$

$(\cos{\theta})^{2} = 1 - \frac{1}{16}$

$(\cos{\theta})^{2} = \frac{16-1}{16}$

$(\cos{\theta})^{2} = \frac{15}{16}$

$\cos{\theta} = \pm \sqrt{\frac{15}{16}}$

Since the angle is in the first quadrant, the cosine is positive.

$\cos{\theta} = \frac{\sqrt{15}}{4}$

3 0

3 years ago

A production process fills containers by weight. Weights of containers are approximately normally distributed. Historically, the

forsale [732]

Answer:

option (c) n = 201

Step-by-step explanation:

Data provided in the question:

Standard deviation, s = 5.5 ounce

Confidence level = 99%

Length of confidence interval = 2 ounces

Therefore,

margin of error, E = (Length of confidence interval ) ÷ 2

= 2 ÷ 2

= 1 ounce

Now,

E = $\frac{zs}{\sqrt n}$

here,

z = 2.58 for 99% confidence interval

n = sample size

thus,

1 = $\frac{2.58\times5.5}{\sqrt n}$

n = (2.58 × 5.5)²

n = 201.3561 ≈ 201

Hence,

option (c) n = 201

5 0

3 years ago

Branda and Laurie have rectangular shaped backyards. Branda's yard measures 35 feet by 90 feet. Laurie's yard measures 40 feet b

tia_tia [17]

To find the area of each backyard, we need to multiply the length and width together.

For Branda, her yard is 35 by 90, which means the area is 35*90 which = 3150.

For Laurie, her yard is 40 by 65, which means the area is 40*65 which = 2600.

Now, we are asked to find the difference between Branda and Lauries yard areas. The difference means how much larger Branda's area is than Lauries.

This means we have to subtract Laurie's area from Branda's.

So, we do 3150 - 2600 = 550

So, our answer is 550ft^2

4 0

3 years ago

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