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 di

Question

3 years ago

10

agram and find the length of the altitude

2 answers:

ki77a [65] · Answer 1 · 2022-02-28T12:18:14+03:00

ki77a [65]3 years ago

7 0

Altitude = 175.6 units

mestny [16] · Answer 2 · 2022-02-28T14:27:12+03:00

Answer:

AD=175.66 units

Step-by-step 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

$\frac{AD}{DC}=tan55^{\circ}$

⇒ $\frac{AD}{123}=1.428$

⇒ $AD=123(1.428)$

⇒ $AD=175.66 units$

Thus, the length of the altitude is 175.66.