A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
The angle of depression of one side of a lake, measured from from a balloon 2500 feet above the lake is 43 degrees. The angle of depression to the opposite side of the lake is 27 degrees. Find the width of the lake.
anonymous
 5 years ago
The angle of depression of one side of a lake, measured from from a balloon 2500 feet above the lake is 43 degrees. The angle of depression to the opposite side of the lake is 27 degrees. Find the width of the lake.

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Draw a picture of a balloon in the air and a lake in the distance.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let the line joining the balloon's observer and his nadir point on the lake be x. The nadir point is that point on the lake that is directly below the balloon's observer. x is normal to the lake's surface, that is, makes a 90 degree angle with the lake's surface. Let y be the join between the observer and the first side of the lake. y is the hypotenuse of a right triangle. The distance between the nadir and the lakes edge is: x Cot[43 Degrees ] = 2500 Cot[Pi 43/180] In a similar manner the distance between the nadir and the opposite side of the lake is: 2500 Cot[Pi 27/180] The sum of the two cotangent expressions is the distance across the lake to the nearest foot: 2500 Cot[Pi 43/180] + 2500 Cot[Pi 27/180]= \[2500 \left(\text{Cot}\left[\frac{43 \pi }{180}\right]+\text{Cot}\left[\frac{3 \pi }{20}\right]\right)=7587 \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank You! Please help me figure this out. The angle of elevation to the top of the radio atenna on the top of a building is 53.4 degrees. After moving 200 feet closer to the building, the angle of elevation is 63.4 degrees. Find the height of the building if the height of the atenna is 189 feet. Please HELP!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Give me a few minutes to look at it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Got the equations, want to check out the answers.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is the first time I have tried to solve a problem in a face book type of environment with an audience. Let x be the distance from the 63 degree measurement position to the base of the building. Now back up 200 feet and you are x+200 feet from the building's base. Let y be the height of the building. Then the top of the antenna is y +189 above the ground. What you have is two equations in two unknowns. The tangent of 53 degrees is (y+189)/(x+200). The tangent of 63 degrees is (y+189)/x The solution for y, the height of the building is: \[y\to 189+\frac{200 \text{Cot}\left[\frac{3 \pi }{20}\right] \text{Cot}\left[\frac{37 \pi }{180}\right]}{\text{Cot}\left[\frac{3 \pi }{20}\right]\text{Cot}\left[\frac{37 \pi}{180}\right]}=630.5 \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Used Mathematica 8 to get you an exact symbolic solution for y.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Used Mathematica 8 to get you an exact symbolic solution for y.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.