Question

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AB=9, and AC=12, find HC.

Answer 1

Answer:

HC = 5.25 units

Step-by-step explanation:

It is given in the ΔABC, ∠ABC = 90°, side BH is the altitude of the triangle.

AB = 9 and AC = 12 units and we have to find the length of HC.

In the right angle triangle ΔABC

$Cosc=\frac{base}{hypotenuse}=\frac{AB}{AC}=\frac{9}{12}$

Now from ΔABH

$cos c=\frac{AH}{AB}$

Since cosine of angle is common in both the triangles.

Therefore $\frac{AH}{AB}=\frac{9}{12}$

$\frac{AH}{9}=\frac{9}{12}$

$AH=\frac{81}{12}=6.75 units$

Since HC = AC - AH = 12 - 6.75 = 5.25 units

Therefore answer will be HC = 5.25 units.

Answer 2

Answer:

5.25

Step-by-step explanation:

H/L = L/S

Hypotenuse/Leg = Leg/Side

12/9 = 9/x

x=6.75

12-6.75 = 5.25