Question

Work out the height of the following triangles

Answer 1

A) height =
`11.3cm` .

B) height =
`15.48cm` .

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= √(128)`

⇒
`Perpendicular= √(2^6(2))`

⇒
`Perpendicular= 2^3√(2)`

⇒
`Perpendicular= 8√(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= √(240)`

⇒
`Perpendicular= 4√(15)cm`

Therefore , height =
`15.48cm` .

Answer 2

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

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 =
`√(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 =
`√(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.