Trigonometry (Formulae)

Question 1

Area for equilateral triangle

Answer 1

∆=√3 x²/4

Question 2

Pythagoras triplets ? 5

Answer 2

1,1,√2
3, 4, 5
5, 12, 13
6, 8, 10
8, 15, 17

Question 3

Scalene triangle

Answer 3

All sides of the triangle are equal.

Question 4

Isosceles triangle

Answer 4

Measurement of two sides are equal

Question 5

Acute angle triangle

Answer 5

The triangle, having all angles less than 90.

Question 6

Obtuse angle triangle

Answer 6

The triangle, having one Angle greater than 90⁰

Question 7

Right angle triangle

Answer 7

Having one Angle 90⁰

Question 8

1. 45⁰—–90⁰ ?
2. 30⁰——90⁰ ?
3. 30⁰——60⁰ ?

Answer 8

1. ×√2 & ÷√2
2. ×2 & ÷2
3. ×√3 & ÷√3

Question 9

If the sides of triangle angels are equal then?

Answer 9

Angles will also be equal

Question 10

Distance between triangle

Answer 10

X=√D1+D2

Question 11

Exterior angle is equal to ?

Answer 11

Sum of the other two (interior angles), except that angle that touches itself.

Question 12

General formula for area of triangle

Answer 12

A=1/2 B×A

Question 14

For finding the area of a triangle, if
Two sides and one angle are given.

Answer 14

1. 1/2 ab sin (ç)
2. 1/2 ac sin (ß)
3. 1/2 bc sin(à)

Question 15

For finding the area of a triangle, if two sides and one angle are given.

Answer 15

1. 1/2 a² sin (ß) sin(ç)/ sin(ã)
   2 1/2 b² sin (ã) sin(ç)/ sin(ß)
   3 1/2 ç² sin (ß) sin(ã)/ sin(ç)

Question 16

Parameters and semi perimeters

Answer 16

Parameters= sum of all sides of triangle.
Semi perameter= sum of all…. /2

Question 17

Law of cosine if sides are given (if you want to find any angle à,ß,ç)

Answer 17

a²=b²+c²-2bc cos à
b²= a²+c² -2ac cos ß
c²= a²+b²-2ab cos ç

All need included angle
C²= 9+16 -2.3.4.cos 30⁰
C=1 ans

P a=3
> Included angle 30⁰
b=4
c=?

Question 18

Theorem of (Z)

Answer 18

Angles become equal in the structure like Z

Question 19

When the angle changes by stepping to the tower. 1 (small) 2(large)

Answer 19

d= h(cot 1- cot2)

Question 20

a/b =
b/c =
a/c =

Answer 20

a/b = sinà/sinß
b/c = sinß/sinç
a/c = sin à/sinç

a=3, b=4,
If à= 30⁰
Sol
3/4 = sin30/sinß
B= sin-¹ 2/3

Question 22

Heroes formula

Answer 22

Heroes formula is used to find area of a ∆ in which all sides are given

∆=√S(S-a) × (S-b) × (S-c)

S= semi perameter

a=3
b=5
c=7 ans= approximately (324) not confirmed

Question 23

Area of equilateral triangle

Answer 23

∆= √3 x² /4

Find area of equilateral triangle, a=4
Ans . 4√3

Question 24

Cirum circle

Answer 24

Circle je pet me triangle
A circle that passes through all vertices of triangle
R=abc/4∆ → for radius of circum circle

If triangle is equilateral?
R=x/√3

Question 25

Inradius

Answer 25

Triangle me circle

r= ∆/s

If triangle is equilateral
r=√3 x/6

Question 26

Described circle

Answer 26

The triangle in which 3 circles touches 3 triangles.

Question 27

Ratios between circles (part 1)

Answer 27

r1,2,3 = escribed circle
Khali r = inradius
R = radius for circum circle

r1×r2×r3= ∆s/rs²
r. r1.r2.r3= r.∆s or ∆² or ∆/s

Question 29

CircumFerence of circle

Answer 29

2πr