Aperson is riding in a hot air balloon. for the first hour, the wind current is a constant 8.25 mph in the direction n37.5°e. then the wind current changes to 6.00 mph and heads the balloon in the direction s52.5°e. what is the bearing of the balloon from its starting point? round your answer to 1 decimal place.

The bearing of the balloon from its starting point = N 71.9° E

Step-by-step explanation:

To find the distance to the starting point, the wind and the height are perpendicular to each other. So, use the Pythagorean Theorem :

(Distance from the starting point)² = 8.25² + 6.00² = 112.56

⇒ Distance = 10.6 miles

Then to determine the bearing y :

Since the original bearing that the balloon set off at was N 37.5° E,  

⇒  y = 37.5° + 34.4°

       = 71.9°

Hence, The bearing of the balloon from its starting point = N 71.9° E

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

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step-by-step explanation: