In the given figure, ∠ABC = ∠BMC = 90°, AB = 3 m,
BC = 4 m, and AC = 5 m. Find the length of side BM.

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Solution

It’s given that ΔABC is a right-angled triangle which is right angled at B and BM ⟂ AC.

now, in ΔAMB and ΔABC
∠B = ∠M = $90^{o}$
∠A = ∠A = Common angle
∠MBA = ∠BCA = angle sum property of triangle

Therefore, ΔAMB ~ ΔABC by AAA theorem

Since ΔAMB ~ ΔABC,
$\frac{A M}{A B} = \frac{M B}{B C} = \frac{B A}{C A}$ as the corresponding sides ratio are equal in similar triangles.

$\frac{A M}{3} = \frac{M B}{4} = \frac{3}{5}$

Hence, BM = 2.4 m

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In the given figure, ∠ABC = ∠BMC = 90°, AB = 3 m, BC = 4 m, and AC = 5 m. Find the length of side BM.

In the given figure, ∠ABC = ∠BMC = 90°, AB = 3 m,
BC = 4 m, and AC = 5 m. Find the length of side BM.