you are at a parade looking up at a large balloon floating directly above the street. you are 60 feet away from a point on the street directly Beneath the balloon. to see the top of the balloon your angle of elevation is 53°. to see the bottom of the balloon your angle of elevation is 29°. what is the total height of the Balloon?
The last response was in 2017, a long time ago...... this is like an old group chat.
see the related questions. Same problem, different numbers.
yuh agreed vv sad :( but like im doing the same question soo
To find the total height of the balloon, we can use trigonometry and the concept of similar triangles.
Let's assume the total height of the balloon is represented by 'h.'
From your vantage point, the angle of elevation to the top of the balloon is 53°. This means that the angle between the horizontal line (the street) and your line of sight to the top of the balloon is 53°.
Using trigonometry, we can form the following equation:
tan(53°) = h / 60
Next, let's consider the angle of elevation to the bottom of the balloon, which is 29°. This means the angle between the horizontal line (the street) and your line of sight to the bottom of the balloon is 29°.
Using trigonometry again, we can form a similar equation:
tan(29°) = (h - x) / 60
where 'x' represents the height from the bottom of the balloon to the street.
Since the balloon is floating directly above the street, the total height 'h' is the sum of the top and bottom heights:
h = (h - x) + x
Simplifying this equation, we get:
h = h
The 'h' on both sides of the equation cancels out, showing that any value of 'x' won't affect the total height of the balloon.
Now, let's solve the equation for the value of 'h' using the first equation we formed:
tan(53°) = h / 60
Re-arranging the equation to solve for 'h,' we have:
h = tan(53°) * 60
Calculating this expression, we find:
h ≈ 75.85 feet
Thus, the total height of the balloon is approximately 75.85 feet.