In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AC=5 and BH=2, find AH and CH.
1 answer:
Answer:
AH = 1 or 4
CH = 4 or 1
Step-by-step explanation:
An altitude divides a right triangle into similar triangles. That means the sides are in proportion, so ...
AH/BH = BH/CH
AH·CH = BH²
The problem statement tells us AH + CH = AC = 5, so we can write
AH·(5 -AH) = BH²
AH·(5 -AH) = 2² = 4
This gives us the quadratic ...
AH² -5AH +4 = 0 . . . . in standard form
(AH -4)(AH -1) = 0 . . . . factored
This equation has solutions AH = 1 or 4, the values of AH that make the factors be zero. Then CH = 5-AH = 4 or 1.
You might be interested in
Step 1.
Calculate measure of angle α:
Step 2.
Calculate what fraction of the angle 360° is the angle α:
Step 3.
Calculate the circumference of the Earth (circle):
Step 4.
The length of arc is equal 1/40 of the circumference:
<h3>Answer: A) 628 miles</h3>
