Eric is hanging a rectangle mirror that has a diagonal of 47 inches with an angle of depression of 60°. How many square inches is the mirror? (round to nearest tenth)
Deloris is wrong, its 956.5
956.5 is right
so what is the answer? lol
the area is height * width:
47sin60° * 47cos60°
vhbj
To find the area of the mirror, we first need to determine the length and width of the rectangle. We can use trigonometry to solve for these values.
The angle of depression of 60° suggests that Eric is looking downward at the top edge of the mirror. This creates a right triangle. The diagonal of 47 inches represents the hypotenuse of the triangle.
We can use the trigonometric function "sine" to find the height (opposite side) of the triangle. Since we have the hypotenuse (47 inches) and the angle of depression (60°), we can set up the equation as follows:
sin(60°) = height / 47
Simplifying the equation, we get:
height = 47 * sin(60°)
Using a scientific calculator, we find that sin(60°) is approximately 0.866. Therefore:
height ≈ 47 * 0.866 ≈ 40.682 inches
Now, using the Pythagorean theorem, we can find the width (adjacent side) of the rectangle. The equation is:
width = √(diagonal^2 - height^2)
Plugging in the values, we have:
width = √(47^2 - 40.682^2)
Calculating this expression, the width ≈ 22.598 inches.
Finally, we can find the area of the mirror by multiplying the height and width:
area = height * width ≈ 40.682 * 22.598 ≈ 920.988 square inches
Therefore, the mirror has an area of approximately 920.988 square inches (rounded to the nearest tenth).