Maggie's brother is 10 years younger than twice her age. The sum of their ages is 32.

The angle of elevation of the top of a pole as seen from a point 13 ft away from the base is double its angle of elevation as se

spayn [35]

The height of the pole above the level of the observer's eyes is 31.42 ft

Let the angle of elevation of the top of the pole from a point 47 ft away be α.

Let the angle of elevation of the top of the pole from the point 13 ft away be β.

Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.

If the height of the pole above the level of the observer's eye is h, we have that

tanβ = tan2α = h/13 and tanα = h/47

From trigonometric identities tan2α = 2tanα/(1 - tan²α)

Substituting the values of the variables into the equation, we have

tan2α = 2tanα/(1 - tan²α)

h/13 = 2h/47 ÷ [1 - (h/47)²]

Dividing through by h, we have

1/13 = 2/47 ÷ [1 - (h/47)²]

Cross-multiplying, we have

1/13 = 2/47 ÷ [1 - (h/47)²]

1 - (h/47)² = 2/47 × 13

1 - (h/47)² = 26/47

(h/47)² = 1 - 26/47

(h/47)² = (47 - 26)/47

(h/47)² = 21/47

Taking square-root of both sides, we have

h/47 = √(21/47)

Cross-multiplyng, we have

h = √(21/47) × 47

h = √(21 × 47)

h = √987

h = 31.42 ft

The height of the pole above the level of the observer's eyes is 31.42 ft

Learn more about height of a pole here:

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4 0

2 years ago

Sam and Harry are family. Sam is currently is three times Harry's age. Sam's age is also 10 more than twice Henry's age. What ar

kramer

Answer:

<em>Sam is 30 years old, and Harry is 10 years old.</em>

Step-by-step explanation:

Let us assume that the age of Sam is x and the age of Harry is y.

Sam is currently is three times Harry's age.

So, $x=3y$ ----------------------1

Sam's age is also 10 more than twice Harry's age.

so, $x=2y+10$ ---------------2

Subtracting 2 from 1, we get

$\Rightarrow x-x=3y-2y-10$

$\Rightarrow 0=y-10$

$\Rightarrow y=10$

putting this in equation 1,

$x=3(10)=30$

Therefore, Sam is 30 years old, and Harry is 10 years old.

6 0

3 years ago

Read 2 more answers

Simplify (1/2)4<br> 1/16<br> 1/8 <br>1/4 <br>which one is correct

miskamm [114]

The correct one is 1/8

7 0

3 years ago

Read 2 more answers

There are 4 sports stores,9 clothing stores and 6 jewelry stores ina shopping crnter which ratio compares the number of sports s

Pani-rosa [81]

The ratio is 2 : 9

Step-by-step explanation:

Given:

The number of sports store = 4

The number of clothing store = 9

The number of jewellery stores = 5

To Find :

The ratio of number of sports stores to the total number of stores

Solution:

The ratio of number of sports stores to the total number of stores

= $\frac{\text{number of sports store}}{\text{ Total number of stores}}$

The total number of stores = number of sports store + number of clothing store + number of jewellery store

The total number of stores = 4 + 9 + 5

The total number of stores = 18

Now the ratio is

= $\frac{4}{18}$ or 4 : 8

The ratio after reduction is

= $\frac{2}{9}$ or 2 : 9 or 2 to 9

7 0

4 years ago

Please Help I Don't Understand!

Nutka1998 [239]

The value of x is 8 from the diagram given.

<h3>How do you calculate the sides of similar triangles?</h3>

The corresponding sides of a similar triangle are said to be in proportion if and only if the corresponding angle are also equal.

To calculate the side of line x (|x|), we have to determine the ratios of the corresponding sides as:

$\mathbf{\dfrac{BC}{DC} = \dfrac{AC}{EC}}$

$\mathbf{\dfrac{x}{10} = \dfrac{12}{15}}$

x = 120/15

x = 8

Therefore, we can conclude that the value of x is 8.

Learn more about calculating similar triangles here:
brainly.com/question/11899908

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4 0

2 years ago