Area related to circle exercise 5.2

See also: These worksheets cover circumferences of circles, and well as introductions to radius and diameter. Find the areas of the triangles using the correct formula. This page will connect you to worksheets on areas of rectangles, parallelograms, trapezoids, and surface area. Here's an index page that will link you to all types of different geometry worksheet topics, including perimeter, plotting points, volume, similar/congruent, polygons, solid shapes, and more.

\( \newcommand \). We state here without proof a useful relation between inscribed and central angles: Theorem 2.4 If an inscribed angle \(\angle\,A\) and a central angle \(\angle\,O\) intercept the same arc, then \(\angle\,A = \frac\,\angle\,O\) (so \(\;\angle\,O = 2\,\angle\,A = 2\,\angle\,D\,) \). We will now prove our assertion about the common ratio in the Law of Sines: Theorem 2.5 For any triangle \(\triangle\,ABC \), the radius \(R\) of its circumscribed circle is given by: \[2\,R ~=~ \frac \). Corollary 2.6 For any right triangle, the hypotenuse is a diameter of the circumscribed circle, i.e. the center of the circle is the midpoint of the hypotenuse. For the right triangle in the above example, the circumscribed circle is simple to draw; its center can be found by measuring a distance of \(2.5\) units from \(A\) along \(\overline\)). Similar arguments for the other sides would show that \(O\) is on the perpendicular bisectors for those sides: Example 2.18 Find the radius \(R\) of the circumscribed circle for the triangle \(\triangle\,ABC\) from Example 2.6 in Section 2.2: \(a = 2 \), \(b = 3 \), and \(c = 4 \). Then draw the triangle and the circle. Solution: In Example 2.6 we found \(A=28.9^\circ \), so \(2\,R = \frac\); their intersection is the center \(O\) of the circle. Use a compass to draw the circle centered at \(O\) which passes through \(A \). Theorem 2.5 can be used to derive another formula for the area of a triangle: Theorem 2.8 For a triangle \(\tria...

A sector is cut from a circle of radius 42cm. The central angle of the sector is 150°. Find the length of the arc. Sol : Given: Radius of a circle, r = 42cm Central Angle of the sector, θ = 150° To find: Length of the arc i.e. AB Now, Length of an arc of a sector of angle θ$=\frac \times 2 \times 22 \times 6$ ⇒Length of an arc of a sector of angle θ = 5×22 =110 cm Q3 | Ex-13 |Class 10 | Area related to circle | KC Sinha Mathematics | Chapter 13| myhelper A pendulum swings through an angle 60° and describes an arc 8.8 cm in length. Find the length of the pendulum $\left[\right.$ Use $\left.\pi=\frac \times 2 \pi r$ $\Rightarrow 8.8=\frac$ ⇒r = 8.4cm Q4 | Ex-13 |Class 10 | Area related to circle | KC Sinha Mathematics | Chapter 13| myhelper A wire made of silver is looped in the form of circular ear ring of radius 5.6 cm. It is rebent into a square form. Determine the length of the side of the square. Sol : Given: Radius of the circle = 5.6cm So, the circumference of the circle = 2πr $=2 \times \frac$ = 8.8cm Hence, the side of a square = 8.8cm Q5 | Ex-13 |Class 10 | Area related to circle | KC Sinha Mathematics | Chapter 13| myhelper $=\frac$ ⇒θ = 48° Hence, the angle subtended by the arc at the centre of the circle is 48° Q6 | Ex-13 |Class 10 | Area related to circle | KC Sinha Mathematics | Chapter 13| myhelper A car has wheels which are 80 cm in diameter. How many complete revolutions does each wheel make in 10 minutes when the car is moving at a speed of 80 km per hour?...

Learning Objectives In this section, you will: • Find function values for the sine and cosine of 30° or ( π 6 ) , 45° or ( π 4 ) 30° or ( π 6 ) , 45° or ( π 4 ) and 60° or ( π 3 ) . 60° or ( π 3 ) . • Identify the domain and range of sine and cosine functions. • Use reference angles to evaluate trigonometric functions. Figure 1 The Singapore Flyer was the world’s tallest Ferris wheel, until being overtaken by the High Roller in Las Vegas and the Ain Dubai in Dubai. (credit: “Vibin JK”/Flickr) Looking for a thrill? Then consider a ride on the Ain Dubai, the world's tallest Ferris wheel. Located in Dubai, the most populous city and the financial and tourism hub of the United Arab Emirates, the wheel soars to 820 feet, about 1.5 tenths of a mile. Described as an observation wheel, riders enjoy spectacular views of the Burj Khalifa (the world's tallest building) and the Palm Jumeirah (a human-made archipelago home to over 10,000 people and 20 resorts) as they travel from the ground to the peak and down again in a repeating pattern. In this section, we will examine this type of revolving motion around a circle. To do so, we need to define the type of circle first, and then place that circle on a coordinate system. Then we can discuss circular motion in terms of the coordinate pairs. Finding Function Values for the Sine and Cosine To define our trigonometric functions, we begin by drawing a unit circle, a circle centered at the origin with radius 1, as shown in t t intercepts fo...