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:

An airplane takes off 200200 yards in front of a 180180 yard building.\newlineFind the angle of elevation for the plane so it does not hit the building.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 6right chevron icon
Understanding integersright chevron icon

Full solution

Q. An airplane takes off 200200 yards in front of a 180180 yard building.\newlineFind the angle of elevation for the plane so it does not hit the building.
  1. Identify Known Values: Identify the known values and the problem to be solved.\newlineWe know the following:\newline- The distance from the plane's takeoff point to the building is 200200 yards.\newline- The height of the building is 180180 yards.\newlineWe need to find the angle of elevation that the plane must have to clear the building without hitting it.
  2. Visualize Problem: Visualize the problem as a right triangle. The building forms a vertical line (height), the distance from the takeoff point to the building forms the horizontal line (base), and the path of the plane forms the hypotenuse. The angle of elevation is the angle between the base and the hypotenuse.
  3. Use Trigonometry: Use trigonometry to find the angle of elevation.\newlineThe tangent of the angle of elevation θ\theta is the ratio of the opposite side (height of the building) to the adjacent side (distance from the takeoff point to the building).\newlineSo, tan⁡(θ)=oppositeadjacent=height of the buildingdistance from takeoff point to building\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\text{height of the building}}{\text{distance from takeoff point to building}}.
  4. Calculate Tangent: Calculate the tangent of the angle of elevation.\newlinetan⁡(θ)=180 yards200 yards\tan(\theta) = \frac{180 \, \text{yards}}{200 \, \text{yards}}\newlinetan⁡(θ)=0.9\tan(\theta) = 0.9
  5. Find Angle: Find the angle of elevation using the arctangent function. \newlineθ=arctan(0.9)\theta = \text{arctan}(0.9)\newlineUse a calculator to find the angle in degrees.
  6. Calculate with Calculator: Calculate the angle using a calculator.\newlineθ≈arctan⁡(0.9)≈41.99\theta \approx \arctan(0.9) \approx 41.99 degrees\newlineThe angle of elevation should be approximately 41.9941.99 degrees for the plane to clear the building.

More problems from Understanding integers

Question
Which of the following is a correct interpretation of the expression −3−5 -3-5 ?\newlineChoose 11 answer:\newline(A) Start at 55 on the number line and move 33 to the left.\newline(B) Start at 55 on the number line and move 33 to the right.\newline(C) Start at −3-3 on the number line and move 55 to the left.\newline(D) Start at −3-3 on the number line and move 55 to the right.
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following is a correct interpretation of the expression −3+(−5)? -3+(-5) ? \newlineChoose 11 answer:\newline(A) The number that is 55 to the left of −3-3 on the number line\newline(B) The number that is 55 to the right of −3-3 on the number line\newline(C) The number that is 33 to the left of 55 on the number line\newline(D) The number that is 33 to the right of 55 on the number line
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following is a correct interpretation of the expression −4+13 -4+13 ?\newlineChoose 11 answer:\newline(A) The number that is 44 to the left of −13-13 on the number line\newline(B) The number that is 44 to the right of −13-13 on the number line\newline(C) The number that is 1313 to the left of −4-4 on the number line\newline(D) The number that is 1313 to the right of −4-4 on the number line
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following is a correct interpretation of the expression 5−8 5-8 ?\newlineChoose 11 answer:\newline(A) Start at 55 on the number line and move 88 to the left.\newline(B) Start at 55 on the number line and move 88 to the right.\newline(C) Start at 88 on the number line and move 55 to the left.\newline(D) Start at 88 on the number line and move 55 to the right.
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following is a correct interpretation of the expression 3+(−7)? 3+(-7) ? \newlineChoose 11 answer:\newline(A) Start at 77 on the number line and move 33 to the left.\newline(B) Start at 77 on the number line and move 33 to the right.\newline(C) Start at 33 on the number line and move 77 to the left.\newline(D) Start at 33 on the number line and move 77 to the right.
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following are true statements about the expression −7+7 -7+7 ?\newlineChoose 22 answers:\newline(A) The expression describes the number that is 77 to the left of −7-7 on the number line.\newline(B) The expression describes the number that is 77 to the right of −7-7 on the number line.\newline(C) The expression equals −14-14 .\newline(D) The expression equals 00.
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following is a correct interpretation of the expression 6−13 6-13 ?\newlineChoose 11 answer:\newline(A) Start at 1313 on the number line and move 66 to the left.\newline(B) Start at 1313 on the number line and move 66 to the right.\newline(C) Start at 66 on the number line and move 1313 to the left.\newline(D) Start at 66 on the number line and move 1313 to the right.
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following are true statements about the expression −9+9 -9+9 ?\newlineChoose 22 answers:\newline(A) The expression describes the number that is 99 to the left of −9-9 on the number line.\newline(B) The expression describes the number that is 99 to the right of −9-9 on the number line.\newline(C) The expression equals −18-18 .\newline(D) The expression equals 00 .
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following is a correct interpretation of the expression −7−(−11)? -7-(-11) ? \newlineChoose 11 answer:\newline(A) Start at −7-7 on the number line and move 1111 to the left.\newline(B) Start at −7-7 on the number line and move 1111 to the right.\newline(C) Start at −11-11 on the number line and move 77 to the left.\newline(D) Start at −11-11 on the number line and move 77 to the right.
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following are true statements about the expression −8+8? -8+8 ? \newlineChoose 22 answers:\newline(A) The expression describes the number that is 88 to the left of −8-8 on the number line.\newline(B) The expression describes the number that is 88 to the right of −8-8 on the number line.\newline(C) The expression equals −16-16 .\newline(D) The expression equals 00 .
Get tutor helpright-arrow

Posted 3 months ago

View all (5)