Question

Find the altitude of an isosceles triangle with a vertex angle (that is, the non-base angle) of 70° and a base of 246. Draw a diagram and find the length of the altitude

Answer 1

altitude = 175.6 units

Answer 2

AD=175.66 units

Explanation:

It is given that ABC is an isosceles triangle in which base is 246 and the non base angle is 70°.

Thus, applying the angle sum property in ΔABC, we get

∠A+∠B+∠C=180°

⇒70°+2∠B=180°

⇒∠B=55°

Thus, ∠B=∠C=55°.

Now, Draw AD perpendicular to BC such that BD=DC=123, then applying trigonometry in ΔADC, we have

`(AD)/(DC)=tan55^(\circ)`

⇒
`(AD)/(123)=1.428`

⇒
`AD=123(1.428)`

⇒
`AD=175.66 units`

Thus, the length of the altitude is 175.66.