A beam tests against a wall, forming a 50 degrees with the floor. Use the function y=9 sec 0 to find the length of the beam to the nearest tenth of a foot.
14.0 ft
11.7 ft
5.8 ft
6.9
B?
14 ft. plug 50° in for theta and solve.
To find the length of the beam, we can use the trigonometric function secθ, where θ is the angle formed with the floor.
Given that the angle formed is 50 degrees, we can use the equation y = 9 secθ.
Substituting the angle into the equation, we get:
y = 9 sec(50)
To find the value of sec(50), we can use a calculator. The value of sec(50) is approximately 1.532.
Substituting this value back into the equation, we get:
y = 9 * 1.532
Simplifying:
y = 13.788
Rounding to the nearest tenth of a foot, the length of the beam is approximately 13.8 feet.
So, the correct answer is 13.8 ft.
To find the length of the beam, we can use trigonometry and the given function y = 9 sec θ, where θ is the angle formed between the beam and the floor.
In this case, the angle formed is 50 degrees. Therefore, we can substitute θ = 50 degrees into the equation y = 9 sec θ.
y = 9 sec 50
y = 9 / cos 50
y = 9 / 0.643
y ≈ 13.978
Therefore, the length of the beam to the nearest tenth of a foot is 14.0 ft.
So the correct option is A) 14.0 ft.