Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
sin²x + cos²x = 1 , then
sin²x = 1 - cos²x and cos²x = 1 - sin²x
Consider the left side
← expand numerator/denominator using FOIL
=
= 
= 
= 
= cot²A = right side , thus proven
Here you would use right triangle trig (SOH CAH TOA)
So first draw a right triangle. Imagine youre standing at the angle opposite the right angle which is the one on the ground.This angle is the 41°. Now Imagine the balloon is as the angle above the right triangle. Well since the balloon is 1503 m from his location this would be the hypotenuse. SInce we are trying to find the height (x) we would use sine since
sine = opposite/hypotenuse . Now lets solve make sure calculator is in degree mode:
sin41 = x/1503 multiply both sides by 1503 to cancel it out
1503sin41 = x plug into calculator
x = 986.057 ft
The balloon is 986.057 feet above the ground.
Answer:
-2x² + 21x + 27
Step-by-step explanation:
distribute 3 to get:
(6x² + 21x + 12) - 8x² + 15
combine 'like terms' to get:
-2x² + 21x + 27
Sq root (54) =
sq root (9*5) =
3 * sq root (5)