A Balloon Is 50m High Its Angle Of Elevation From Observer A Is 45 And From Observer B It Is 30 What Is The Maximum Distance Between The Two Observers

a balloon is 50m high its angle of elevation from observer A is 45 and from observer B it is 30 what is the maximum distance between the two observers? express your answer the nearest meter.

 

Answer:

37 meters

Step-by-step explanation:

Step 1. Draw the problem

Our first step in solving this problem is drawing the problem for us to visualize and understand it.  

The height of balloon is given which is 50 m, and the angles of elevation of observers A and B from the balloon are also given.

We let "x" be the distance between observer A and B

We let "a" be the distance of observer A from the balloon

We let "b" be the distance of observer B from the balloon  

You can see the sketch I made for this problem below.

Step 2: Understand the problem

In the problem we are given 2 angles of elevation, 45° for observer A and 30° for observer B, and one height which is 50 m. We can separate these angles to form 2 triangles with same height but different angle of elevation.  

A second sketch is provided below for this step.

Step 3: Know the mathematical concept

Now that we can see the sketch the next step is to know what mathematical concept is needed here. Based on the sketch, the problem formed right triangles, so we have to use formulas related to right triangles and Pythagorean theorem.

Step 4: Use the formula

For us to be able to solve for the sides of a right triangle given an angle, we can use the concept of trigonometry, the SOH CAH TOA.

S is sine, C is cosine, T is tangent, O is opposite, H is hypotenuse, and A is adjacent.

An image is provided in order for us to see the relation of this SOH CAH TOA to the right triangles.

Step 5: Solve

Using the information from step 4, we can now solve for the missing adjacent sides of the 2 triangles we have in step 2.

Solving for a:

tan (45) = 50/a

(a)*(tan(45)) = 50

a = 50/(tan⁡(45))

a = 50 m

Solving for b:

tan (30) = 50/b

(b)*(tan(30)) = 50

b = 50/(tan⁡(30))

b = 50√3 m  = 86.60254 m

Solving for x which is the distance between observers A and B:

x = b - a

x = 50√3 m - 50 m

x = 36.60254 m

Expressing the answer in nearest meter, the final answer is 37 m.

To learn more about right triangles, trigonometry, and Pythagorean theorem, you can visit the following:

brainly.ph/question/2140443

brainly.ph/question/81753

brainly.ph/question/1495403





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