Question

If in a ΔABC, the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in ______

पर्याय

• G. P.

• A. P.

• A.P - G.P.

• H. P.

Answer 1

If in a ΔABC, the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in A. P.

Explanation:

Let altitudes from A, B and C be p₁, p₂ and p₃ resp.

∴ Δ = `1/2 p_1a = 1/2 p_2b = 1/2 p_3b`

Given that, p₁, p₂, p₃, are in H.P.

`\implies (2Δ)/a, (2Δ)/b, (2Δ)/c` are in H.P.

`\implies 1/a, 1/b, 1/c` are in H.P.

`\implies` a, b, c are in A.P.

By sine formula

`\implies` K sin A, K sin B, K sin C are in AP

`\implies` sinA, sinB, sinC are in A.P.