Question

How do I draw the right triangle ABC whose sides have the following values given below, and then find the six trigonometric functions of angle A? a = 2, b= √5, c = 3

Answer 1

Steps for construction

1. Line segment `CB=2cm` is cut off from a straight-line `CX` with the help of a compass.
2. `CY` is drawn perpendicular on `CX` at C.
3. The line segment `BA=3cm` is cut off by drawing an arc of radius of `3cm` centering B using a compass.
4. A,B are joined using ruler. Now i `Delta ABC` is the required triangle ,where we have

`BC=2cm, AB=3cm and /_ACB=90^@`

So `CA=sqrt(AB^2-BC^2)=sqrt(3^2-2^2)=sqrt5` cm

Now 6 trigonometric ratios of angle `A` will be

`sinA=(BC)/(AB)=2/3=>cscA=3/2`

`cosA=(AC)/(AB)=sqrt5/3=>secA=3/sqrt5`

`tanA=(BC)/(AC)=2/sqrt5=>cotA=sqrt5/2`