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ASHA 777 [7]
3 years ago
9

Carol is standing 8 feet from a lamppost. The angle of elevation from her eyes to the top of the lamppost is 20o, and the angle

of depression from her eyes to the bottom of the post is 35o . How tall is the lamppost?
Mathematics
1 answer:
kupik [55]3 years ago
8 0

Answer:

Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft

Step-by-step explanation:

The illustration form a triangle that can be demarcated into 2 right angle triangle. One triangle representing depression triangle and the other elevation triangle.

Depression triangle

The opposite side of the triangle formed is the length of the pole from the base to the horizontal line of sight. Therefore,

using tangential ratio

tan 35° = opposite/adjacent

tan 35° = a/8

cross multiply

a = 8 tan 35°

a = 8 × 0.70020753821

a = 5.60166030568

a = 5.602 ft

Elevation triangle

The opposite side of this right angle triangle represent the length from the horizontal line of sight to the top of the lamppost.

tan 20° = opposite/adjacent

tan 20° = b/8

cross multiply

b = 8 tan 20°

b = 8 × 0.36397023426

b = 2.91176187413

b = 2.912 ft

Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft

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In a 30cm by 25cm rectangle, a quadrant of a circle of radius 7cm has been cut away from each corner. What is the perimeter of t
lidiya [134]

Answer:

Perimeter = 98 cm

Area = 596 cm^{2}

Step-by-step explanation:

Please refer to the attached image for the resultant figure when a quadrant of circle with radius 7 cm is cut from a rectangle of sides 30 cm and 25 cm.

Perimeter of a figure = Sum of all its sides + Perimeter of circle

Quadrant of a circle is one fourth of a circle and there are 4 such quadrant of a circle, so eventually there is one complete circle in this figure.

The sides of this resultant figure = 30 - 14 = 16 cm

and 25 - 14 = 11 cm

So perimeter of this figure = 16 + 11 + 16 + 11 + Perimeter of circle

\Rightarrow 54 + 2 \pi r\\\Rightarrow 54 + 2 \times \dfrac{22}{7} \times 7\\\Rightarrow 54 + 44 = 98 cm

To find area of this figure = Area of rectangle - Area of circle

Area of rectangle = Length \times Width

\Rightarrow 30 \times 25 = 750\ cm^{2}

Area of circle = \pi r^{2}

\Rightarrow \dfrac{22}{7} \times 7^{2} = 154\ cm^{2}

So, area of figure = 750 - 154 = 596 cm^{2}

3 0
3 years ago
What is the Gcf for 39,6
andreev551 [17]

Answer:

The greatest common factor of these two numbers is 3

Step-by-step explanation:

To find this, look for the highest number that both can be divide by to get whole numbers.

39/3 = 13

6/3 = 2

6 0
3 years ago
This is one question. Algebra 2 transformations
Talja [164]

Answer:

End result is ln(-x) + 1

Step-by-step explanation:

1,  ln x + 2

2. ln(x + 2) + 2

3. ln(x + 2 - 2) + 2 = ln x + 2

4. ln x + 1

5. ln(-x) + 1

8 0
3 years ago
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Suppose there are 1,000 total sales representatives in the midwest and northeast regions, with 500 sales re
Maru [420]

Making 20 groups of 10 is the sampling strategy that can be used to select 200 sales representatives.

What is sampling?

Sampling is the phrase used to describe a statistical procedure in which a predetermined number of observations are chosen from a larger population. More precisely, sampling can be described as the process of choosing a portion of a statistical population in order to estimate the characteristics of the entire population. Samples that are representative of the population under study are sought for by statisticians.

Making 20 groups of 10 is the most effective way of sampling that can be employed here for the sales director to incorporate 200 sales representatives in this situation, with an equal amount of representatives from each region.

Learn more about sampling here:

brainly.com/question/11045407

#SPJ4

4 0
2 years ago
Suppose a six-sided die is tossed 1200 times and a 6 comes up 419 times. (a) Find the empirical probability for a 6 to occur. (E
krok68 [10]

Answer:

Here both probabilities are not equal.

Therefore the die is not fair and biased.

Step-by-step explanation:

Now n= 1200 times and x = 419 times.

a) Empirical Probability:

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Probability = 0.349

b) Theoretical Probability:

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Here both probabilities are not equal.

Therefore the die is not fair and biased.

3 0
3 years ago
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