Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Un avión vuela a una altitud constante de 10,000 metros. Desde un punto en el suelo, un observador ve al avión con un ángulo de elevación de 30 grados. Calcula la distancia horizontal desde el observador hasta el avión.

Un avión vuela a una altitud constante de 1010,000000 metros. Desde un punto en el suelo, un observador ve al avión con un ángulo de elevación de 3030 grados. Calcula la distancia horizontal desde el observador hasta el avión.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Sum of finite series not start from 1right chevron icon

Full solution

Q. Un avión vuela a una altitud constante de 1010,000000 metros. Desde un punto en el suelo, un observador ve al avión con un ángulo de elevación de 3030 grados. Calcula la distancia horizontal desde el observador hasta el avión.
  1. Use Trigonometry: Use trigonometry to find the horizontal distance. The relationship between the angle of elevation, the altitude of the plane, and the horizontal distance is given by the tangent function.
  2. Set up Equation: Set up the equation using the tangent of 3030 degrees, which is equal to the opposite side (altitude) over the adjacent side (horizontal distance).tan⁡(30∘)=altitudehorizontal_distance\tan(30^\circ) = \frac{\text{altitude}}{\text{horizontal\_distance}}
  3. Plug in Altitude: Plug in the altitude of the plane, which is 10,00010,000 meters.\newline\tan(30°) = \frac{10,000}{\text{horizontal_distance}}
  4. Calculate Tangent: Calculate the tangent of 3030 degrees. The exact value of tan⁡(30°)\tan(30°) is 1/31/\sqrt{3} or 3/3\sqrt{3}/3.\newlinetan⁡(30°)=3/3\tan(30°) = \sqrt{3}/3
  5. Substitute Value: Substitute the value of tan⁡(30°)\tan(30°) into the equation.3/3=10,000/horizontal_distance\sqrt{3}/3 = 10,000 / \text{horizontal\_distance}
  6. Solve for Distance: Solve for the horizontal distance by multiplying both sides by horizontal_distancehorizontal\_distance and then dividing both sides by 3/3\sqrt{3}/3.\newlinehorizontal_distance=10,000(3/3)horizontal\_distance = \frac{10,000}{(\sqrt{3}/3)}
  7. Simplify Equation: Simplify the equation by multiplying the numerator and denominator by 33.horizontal_distance=(10,000×3)3\text{horizontal\_distance} = \frac{(10,000 \times 3)}{\sqrt{3}}
  8. Calculate Distance: Calculate the horizontal distance. horizontal_distance=30,0003horizontal\_distance = \frac{30,000}{\sqrt{3}}
  9. Simplify Square Root: Simplify the square root of 33 to its decimal form, which is approximately 1.7321.732. \newlinehorizontal_distance=30,0001.732\text{horizontal\_distance} = \frac{30,000}{1.732}
  10. Perform Division: Perform the division to find the horizontal distance. horizontal_distance=17,320.50807568877horizontal\_distance = 17,320.50807568877 (This is the wrong calculation, the correct one should be 30,0001.732≈17,320.50807568877\frac{30,000}{1.732} \approx 17,320.50807568877)

More problems from Sum of finite series not start from 1

Question
Find the sum of the finite arithmetic series. ∑n=110(7n+4)\sum_{n=1}^{10} (7n+4)\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`
Get tutor helpright-arrow

Posted 1 month ago

Question
Type the missing number in this sequence: `2, 4 8`, ______,`32`
Get tutor helpright-arrow

Posted 2 months ago

Question
What kind of sequence is this? 2,10,50,250,…2, 10, 50, 250, \ldots Choices:Choices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the missing number in this pattern? 1,4,9,16,25,36,49,64,81,____1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
Get tutor helpright-arrow

Posted 1 month ago

Question
Classify the series. ∑n=012(n+2)3 \sum_{n = 0}^{12} (n + 2)^3 \newlineChoices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the first three partial sums of the series.\newline1+6+11+16+21+26+⋯1 + 6 + 11 + 16 + 21 + 26 + \cdots\newlineWrite your answers as integers or fractions in simplest form.\newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the third partial sum of the series. \newline3+9+15+21+27+33+⋯3 + 9 + 15 + 21 + 27 + 33 + \cdots\newlineWrite your answer as an integer or a fraction in simplest form. \newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the first three partial sums of the series. \newline1+7+13+19+25+31+⋯1 + 7 + 13 + 19 + 25 + 31 + \cdots\newlineWrite your answers as integers or fractions in simplest form. \newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Does the infinite geometric series converge or diverge?\newline1+34+916+2764+⋯1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots\newlineChoices:\newline[A]converge\text{[A]converge}\newline[B]diverge\text{[B]diverge}
Get tutor helpright-arrow

Posted 1 month ago

View all (97)