6.7k views
10 votes
PLEASE ANSWER ASAP TY

In triangle ABC below, BD is the altitude. Find the length of DC. Leave your answer in
simplified radical form.

PLEASE ANSWER ASAP TY In triangle ABC below, BD is the altitude. Find the length of-example-1
User Yuan Wen
by
7.0k points

1 Answer

4 votes

Answer:

Explanation:

Step 1: Find AB Use Pythagoras Theorem

AB =
\sqrt{AC^(2) -BC^(2) } = \sqrt{12^(2) -8^(2) } = √(80)

Step 2: Find the Area of the triangle ABC

Area =
(1)/(2)AB.BC = (1)/(2)√(80).8 = 4√(80) =
16√(5)

Step 3: Find BD. Use the area of the triangle above

Area =
(1)/(2)BD.AC

We already known the Area and AC so, we just plug all the number in

BD =
(2. Area)/(AC) =
(2.16√(5))/(12) =
(8√(5))/(3)

Step 4: Find DC. Use Pythagoras Theorem of the triangle BDC

DC =
\sqrt{BC^(2)-BD^(2) } =
\sqrt{8^(2)-((8√(5))/(3))^(2)} =
(16)/(3)

User Mallory
by
6.4k points