If the diagonal of a rectangular sundeck makes an angle of 67 degrees with one side of the deck and the length of the diagonal is 24 feet,what are the dimensions, to the nearest foot, of the sundeck?
I would do this with trig:
x=24*sin67
y=24*cos67
i don't know sorry.
To solve this problem, we can use trigonometric functions such as sine, cosine, or tangent. Let's consider the given information and draw the rectangular sundeck.
We know that the diagonal makes an angle of 67 degrees with one side of the deck. Let's label the length of the side adjacent to the angle as "a" and the length of the other side as "b." The diagonal, which is 24 feet, represents the hypotenuse of this right triangle.
Using the trigonometric function cosine (cos), we can relate the angle and the lengths of the sides:
cos(angle) = adjacent / hypotenuse
cos(67) = a / 24
To find "a," we rearrange the equation:
a = cos(67) * 24
Using a calculator, we can find that cos(67) is approximately 0.410 and solve for "a":
a ≈ 0.410 * 24
a ≈ 9.84 feet
Therefore, the length of the side adjacent to the angle is approximately 9.84 feet.
To find the length of the other side, we use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides:
24^2 = a^2 + b^2
Simplifying this equation:
576 = 9.84^2 + b^2
Solving for "b" by subtracting 9.84^2 from both sides:
b^2 = 576 - (9.84)^2
Calculating the right side of the equation:
b^2 ≈ 576 - 96.3456
b^2 ≈ 479.6544
Taking the square root of both sides, we can find "b":
b ≈ √(479.6544)
Using a calculator, we find that b ≈ 21.929 feet.
Therefore, the dimensions of the sundeck, to the nearest foot, are approximately 9.84 feet by 21.929 feet.