In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AH=4 and HC=1, find BH.

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sqdancefan sqdancefan · Answer 1 · 2019-02-04T09:42:21+01:00

Answer:

BH = 2

Step-by-step explanation:

The altitude divides the triangle into similar triangles. The ratio of the long side to the short side is the same for all, so ...

AH/BH = BH/HC

4/BH = BH/1

4 = BH² . . . . multiply by BH

2 = BH . . . . . take the square root

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abidemiokin abidemiokin · Answer 2 · 2021-11-29T12:54:30+01:00

The measure of BH from the given diagram is 2

In order to get the measure of BH, we will use the similarity theorem of a triangle as shown:

From the triangle

AH/BH = BH/HC

Given the following parameters

AH=4

HC=1

Substitute the given parameters into the expression above to have:

4/BH = BH/1

Cross multiply

BH^2 = 4 * 1

BH^2 = 4

BH = √4

BH = 2

Hence the measure of BH from the given diagram is 2

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