A diagonal of a rectangle is 8cm and forms an angle measuring 30 with one side. Find the area of a rectangle
Let's first draw the picture. The diagonal of your rectangle will be a line that goes from the top left corner of your rectangle to the bottom right corner. This line is the hypotenuse of your RIGHT triangle. The problem tells us that the hypotenuse forms a 30 degree angle with on of the sides. We can pick either side, but I chose to pick the side that includes the left side of the rectangle. Now, we have a 30-60-90 right triangle. The base of the triangle is opposite the 30 degree angle, so it will equal x. The hypotenuse is 2x and the height is x√3.
SO, since we know the hypotenuse is 8cm, we know: 8=2x and x=4; x√3=4√3
The area of a rectangle is b*h, so we multiple 4√3*4 to give us 16√3
Hope that helps!
I think the answer to this question is 1152
Part 1) <span>angles congruent to <1
we know that
</span><4=<1-------> by vertical angles
<5=<1-------> by corresponding angles
<8=<5------> by vertical angles or <8=<1 ----> by alternate exterior angles
so
the answer part 1) is
<span><4,<8,<5
</span>
Part 2) <span>angles congruent to <2
</span>we know that
<3=<2-------> by vertical angles
<6=<2-------> by corresponding angles
<7=<6------> by vertical angles or <7=<2 ----> by alternate exterior angles
so
the answer part 2) is
<span><3,<7,<6
</span>
Part 3)<span>angles congruent to <7
</span>we know that
<6=<7-------> by vertical angles
<3=<7-------> by corresponding angles
<2=<3------> by vertical angles or <2=<7 ----> by alternate exterior angles
so
the answer part 3) is
<span><3,<6,<2
Part 4) </span><span>angles congruent to <6
</span>we know that
<7=<6-------> by vertical angles
<2=<6-------> by corresponding angles
<3=<2------> by vertical angles or <3=<6 ----> by alternate interior angles
so
the answer part 4) is
<span><3, <7, <2</span>
To illustrate the problem, refer to the following diagram, made with the ever-helpful notepad application:
|\ | \ | \h| \ | \ | \ |_____q\ x
Pretending as if that is a wonderfully-drawn triangle, we are given the distance x of the observer from the launch pad. The angle q is also stated, and is located in the diagram as shown. To look for the distance h of the tip of the rocket to the ground, we consider the following trigonometry function:
tan q = h/x
Since we are solving for h, we multiply both sides with x, giving us:
h = x * tan q
Among the choices, the correct answer is C.
It is a right triangle so,
a² + b² = x²
9² + 12² = x²
225 = x²
√225 = x
15 = x
Hope this helps :)