Use the fact that trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
2 answers:
You might be interested in
The sum of angles in any quadrilateral, including trapezoid, is 360⁰.
Because we have <span>an isosceles trapezoid, we have 2 angles with measure 135⁰,
and we have 2 equal acute angles with measure x⁰.
So, we can find value of acute angle,
135*2 +2x =360⁰
270+2x=360
2x=360-270
2x=90
x=45⁰
So, acute angles in trapezoid = 45⁰.
From triangle ABC,
angle ACB =90⁰
angle A=45⁰,
so angle ABC= 180-(90-45)=45⁰
Triangle ABC is isosceles triangle,so |AC| = |CB|= 5 in.
So, longer base AA' = 5+4+5= 14 in
Now, we can find area of trapezoid.
shorter base = 4 in
longer base = 14 in
altitude =h = 5 in
Area of trapezoid =(1/2)(base1+base2)*h
Area of trapezoid = (1/2)(4+14)*5= 9*5=45 in²
Answer is 45 in².</span>
Because we have <span>an isosceles trapezoid, we have 2 angles with measure 135⁰,
and we have 2 equal acute angles with measure x⁰.
So, we can find value of acute angle,
135*2 +2x =360⁰
270+2x=360
2x=360-270
2x=90
x=45⁰
So, acute angles in trapezoid = 45⁰.
From triangle ABC,
angle ACB =90⁰
angle A=45⁰,
so angle ABC= 180-(90-45)=45⁰
Triangle ABC is isosceles triangle,so |AC| = |CB|= 5 in.
So, longer base AA' = 5+4+5= 14 in
Now, we can find area of trapezoid.
shorter base = 4 in
longer base = 14 in
altitude =h = 5 in
Area of trapezoid =(1/2)(base1+base2)*h
Area of trapezoid = (1/2)(4+14)*5= 9*5=45 in²
Answer is 45 in².</span>
Answer:
<h2>The height is 3.43 centimeters, approximately.</h2>Step-by-step explanation:
Notice that there are 16 pieces from the circle, which means each sector has an angle of
Where all sectors have equal area.
Now, the area of the whole circle is , if we use the formula of its area, we'll find the radius of the circle
Notice that each piece works as an isosceles triangle, because each side is the radius, that is, they have the same length. So far, we know the sides of the isosceles triangle and one internal angle.
To find the height of the one piece, we need to use trigonometric reasons, because the height divides a triangle in two equal right triangles.
Therefore, the height is 3.43 centimeters, approximately.