Tangents

Tanisha Pal Singh

20 Feb 2019

The tangent line to a plane circle at a given point is the straight line that “just touches” the circle at that point. As it passes through the point where the tangent line and the circle meet is called point of tangency.

In the picture above, line L is tangent to the circle with centre O. The point of tangency is point P.

Eportfolio 2/14/19

Tanisha Pal Singh

13 Feb 2019

1)

We have to find out angle A. We know that if two inscribed angles of a circle intercept the same arc or congruent Arcs, then the angles are congruent. So angle A and D would be equal. Then we will set 6y-2 and 5y+8 equal to eachother and we will find out the value of y. Then to find out measure of angle A, we will put the value of y which would be 10 in the equation 6y-2. That will give us the measure of angle A as 58.

2)

We have to find put angle G. We know that if a quadrilateral is inscribed in a circle, opposite angles are supplementary. So we are going to set up as 8x+1+11x+8=180. We will get the value of x as 9. Then to find out angle G, we will put the value of x as 9 in the equation 8x+1. The measure of angle G would be 73.

3)

We have to find put the value of x. We know that if arcs are congruent then chords are congruent. We will set 6x and 2x+24 equal to eachother and then find out the value of x. So 6x-2x=24. 4x=24. x=6. So value of x is 6.

Eportfolio 1/24/19

Tanisha Pal Singh

22 January 2019

Problem 1- We should know the formula arc= angle for this problem. i) We have to find out arc KL. We have been given LM as 67 and NM as 90 and we know sum of angles of straight line is 180. So KL, LM and NM are forming 180. We will add LM and NM and subtract from 180 which will give us KL.

ii) We have to find out LON which is equal to KL and KN. We already know KL as 23 and we know straight angle is 180. So we will add 23 and 180 which will give us 203 which is LON.

iii) We have to find out OM. OM would be equal to ON and NM. We know ON would be equal to KL because they are vertically opposite and KL is 23. So we will add 23 and 90 which will give us the value of OM as 113.

iv) We have to find out KNL. We know sum of angles in circle is 360 and we know KL also. So we can subtract 23 from 360 which will give us KNL as 337.

v) We have to find out NL. We have been given LM as 67 already and NM as 90. So we will add both of those to get NL.

Problem 2- We have been given diameter as 19 feet and the angle PQ as 128. We will find angle QR by subtracting 128 from 180 which will give us 52. We will use arc length formula to solve further. l=x÷360×2×pie×r OR l=x÷360×pie×d. We will plug in the values where x would be the angle and d would be diameter. We will get our length as 34.985 feet.

Problem 3- We have been first given a triangle in which we have been given perpendicular and base and we have to find out the hypotenuse which would be the diameter of the circle. We will use Pythagorean theorem and will find out hypotenuse which would be 25cm. The formula of circumference is pie multiplied by diameter or we can also do 2× pie×r. We can do pie× 25cm which will give us the circumference as 78.539cm.

Central Angles, Circumference and diameter

Tanisha Pal Singh

16 Jan 2019

Central angle is an angle that has it’s vertex on the centre of the circle and has it’s ends on the circle. Arc= Angle. The sum of central angles of the circle measures 360 degrees. Circumference is measuring outside the circle and it’s formula is 2× pie× r, where r is radius or pie× d, where d is diameter. A diameter is a chord that passes through the centre and has both ends on the circle and is made up of collinear radii. d=2×r OR r=d÷2

Winter holidays

Tanisha Pal Singh

9 Jan 2019

In my winter holidays, I had gone to New Mexico, Texas, Grand Canyon, Las Vegas, Los Angeles, San Diego and San Antonio with my parents. I spent my christmas at Las Vegas and my New year at San Antonio. On Christmas, we had eaten dinner at top of the stratosphere in Las Vegas. On new year’s day we had done the river walk in San Antonio. We had also seen the shooting places of topgun movie in San Diego.

Major grade eportfolio

Tanisha Pal Singh

10 December. ( Another response)

1)

1) A ladder is leaning against the house which will be the hypotenuse. It forms 67 degree angle with the ground. The foot of the ladder is 18 feet away from the house which will make the base 18. We have to find the length of the ladder which will be the height. Now we have been given two values and we have to think of a formula which will put values in correct position and we will be able to find out x. The appropriate formula would be cos= adjacent ÷ hypotenuse. We will put values and we will solve. So cos 67 would be equal to 18÷ x. Then we would have to do cos 67 in our calculator, which would be 0.39 . 0.39 would be equal to 18÷ x. Now we have to find x. So x is equal to 18÷ 0.39 . x is equal to 46.153 .

2)

We have to find out x which is perpendicular and we have been given hypotenuse and base as 17 and 13 respectively. The formula is P^2 + B^2 = H^2 . Now we will plug it in. So P^2 + 13^2 = 17^2 . Now we will solve. So P^2 + 169= 289. P^2= 289- 169. P^2= 120. We are looking for P. So we will put in calculator square root of 120 which will come 10.954 and that will be our x.

3)

We have to find out x which is opposite and we have been given adjacent as 22 and we have been given theta as 15. Now we have to think of a formula which will put opposite and adjacent and theta in a formula. Tan is equal to opposite÷ adjacent. Now we will plug in values. So Tan 15 is equal to x divided by 22. Tan 15 we will put in calculator and it would be equal to 0.268 . Now 0.268 would be equal to x divided by 22. So x is equal to 0.268 multiplied by 22 and x will be equal to 5.896

4)

We have been given two sides and we have to find out theta. We have been given opposite and hypotenuse as 18 and 25 respectively. So we will use sin formula because sin is equal to opposite divided by hypotenuse. Now we will plug in. So theta is equal to 18 divided by 25. Theta is equal to 0.72 . x is equal to inverse of sin multiplied by 0.72 . Theta will be equal to 46.054

5 a)

We have been given angle C and sides a as 30 and b as 20. We have to find out side c. Law of cosines in this case will be c^2= a^2 + b^2 – 2ab × cos C

c^2= 30^2+ 20^2- 2 × 30 × 20× cos 59.

c^2 will be equal to 900 plus 400 minus 1200 multiplied by 0.515 . c^2 will be equal to 1300 minus 618 which will be equal to 682. We have to find out c, so we will put square root of 682 which will be equal to 26.115

5b)

We have to find out angle A using law of sines. We have side a, side c and angle C. So side a divided by sin A is equal to side c divided by angle C. We will plug in the values. 30 by sin A is equal to 26.115 by sin 59 which will be equal to 0.857 . Now we will cross multiply, so 0.857 multiplied by 30 is equal to 26. 115 multiplied by sin A . So sin A is equal to 25.71 divided by 26.115. Sin A is equal to 0.984 . A is equal to 79.737

5c)

W have been given angle A and angle C as 79.737 and 59 respectively. A+ B + C is equal to 180. Every triangle is equal to 180 degree total. So now we will plug in, 79.737+ B+ 59= 180

138.737+ B= 180

B will be equal to 180 minus 138.737. So Angle B will be equal to 41.263

Major grade eportfolio

Tanisha Pal Singh

3 Dec 2018

1) Cos 67= 18÷ x

0.39= 18÷ x

x= 18÷ 0.39

x= 46.153 feet

2) P^2 + B^2= H^2

x^2 + 13^2 = 17^2

x^2 + 169= 289

x^2= 289- 169

x^2= 120

x= √120

x= 10.954

3) Tan 15= x÷ 22

0.268= x÷22

x= 0.268×22

x= 5.896

4) Sin = 18÷ 25

Sin theta= 0.72

Theta= sin^-1 ( 0.72)

Theta= 46.054

5a) c^2= a^2+ b^2- 2ab× Cos C

c^2= 30^2+ 20^2- 2(30) (20) × Cos 59

c^2= 900+ 400 – 1200× 0.515

c^2= 1300-618

c^2= 682

c= 26.115

5b) a÷ Sin A= c÷ Sin C

30÷ Sin A= 26.115÷ Sin 59

30÷ Sin A= 26.115 ÷ 0.857

Now we are going to cross multiply

0.857×30= 26.115( Sin A)

25.71= 26.115( Sin A)

25.71÷ 26.115=Sin A

0.984= Sin A

Sin ^-1(0.984)= A

79.737°= A

5c) A+ B + C = 180

79.737+ B+ 59= 180

138.737+ B= 180

B=180- 138.737

B= 41.263