Question

Work out the height of the following triangles

Answer 1

The height of first (a) triangle is 11.31 cm and the height of the second (b) triangle is 15.49 cm.

Step-by-step explanation:

The given is,

             Triangle (a) and (b)

Step:1

              For first (a) triangle

              (Ref the attachment (a))

                          b = 4 cm

                      hyp = 12 cm

              From Pythagoras theorem,

                    $Hyp^{2} = b^{2} +h^{2}$...........................(1)

              Equation becomes,

                    $12^{2}$ = $4^{2}$ + $h^{2}$

                  144 = 16 + $h^{2}$

                     h = $\sqrt{128}$

                     h = 11.314 cm

Step:2

        For first (b) triangle

              (Ref the attachment (b))

                          b = 7 cm

                      hyp = 17 cm

              From Pythagoras theorem,

                    $Hyp^{2} = b^{2} +h^{2}$...........................(1)

              Equation becomes,

                    $17^{2}$ = $7^{2}$ + $h^{2}$

                  289 = 49 + $h^{2}$

                     h = $\sqrt{240}$

                     h = 15.492 cm

Result:

      The height of first (a) triangle is 11.314 cm and the height of the second (b) triangle is 15.492 cm.

       

Answer 2

A) height = $11.3cm$ .

B)   height = $15.48cm$ .

Step-by-step explanation:

Here , We need to calculate height of triangles let's do this :

A)

We draw a perpendicular from vertex to base line (8 cm ) , so length becomes 4 cm of base of triangle .

By Pythagoras Theorem we have ,

$Hypotenuse^2 = Perpendicular^2+Base^2$

⇒ $Hypotenuse^2 = Perpendicular^2+Base^2$

⇒ $12^2 = Perpendicular^2+4^2$

⇒ $144 = Perpendicular^2+16$

⇒ $Perpendicular^2= 144-16$

⇒ $Perpendicular= \sqrt{128}$

⇒ $Perpendicular= \sqrt{2^6(2)}$

⇒ $Perpendicular= 2^3\sqrt{2}$

⇒ $Perpendicular= 8\sqrt{2}cm$

Therefore , height = $11.3cm$ .

B)

We draw a perpendicular from vertex to base line (14 cm ) , so length becomes 7 cm of base of triangle .

By Pythagoras Theorem we have ,

$Hypotenuse^2 = Perpendicular^2+Base^2$

⇒ $Hypotenuse^2 = Perpendicular^2+Base^2$

⇒ $17^2 = Perpendicular^2+7^2$

⇒ $289= Perpendicular^2+49$

⇒ $Perpendicular^2=289-49$

⇒ $Perpendicular= \sqrt{240}$

⇒ $Perpendicular= 4\sqrt{15}cm$

Therefore , height = $15.48cm$ .