Question

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. BC=9 and HC=3, find AH.

Answer 1

Heya mate,

Here is your answer,. ⬇️⬇️

${ANSWER :-}$

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$<i>$ Here we have that,

Let, angle BAC = x

Thus, angle BCA = 90 - x

Now, Thus, angle HBC = x

So, angle BCH = 90 - 3

From the above information, we can say that HBA and BCH are similar triangles.

We know that in similar triangles, the ratio of sides is equal.

Thus, at last we get that,

AH/9 = 9/3

=> AH = 9 * 3 = 27.

➡️ Hence, AH = 27 cm.

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$<b>$ Hope this helps,.

If helps, please mark it as brainliest.

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REGARDS, ARNAB ✌️

THANK YOU

Answer 2

Step-by-step explanation:

BH is altitude means it's a perpendicular height from point B to side AC.

Now we hv two triangles ABH and BCH

In trBCH using Pythagoras

BH= √54 cm

In trABC Pythagoras

AB^2=AC^2-81 Eq-1

Put AC=AH+3

In trABH using Pythagoras

AB^2=BH^2+AH^2. Eq2

BH^2=54

Using Eq1 and Eq2

AH=7.5 cm