In ΔABC, with the usual notations, if sinBsinC=bc/(a^2), then the triangle is ….

Correct answer: (A) Right angled triangle. Key Idea Use sine rule, i.e. a/sinA=b/sinB=c/sinC Given, sinBsinC=bc/(a^2) ⇒a^2=bc/sinBsinC ⇒a^2=b/sinBc/sinC ⇒a^2=a^sinA2 ⇒sin^2A=1 ⇒sinA=1=sin90^o ⇒A=90^o

Q88 / 150 · MHT CET 2019 (Shift 1) · Mathematics

In $Δ A B C,$ with the usual notations, if $s i n B s i n C = \frac{b c}{a^{2}},$ then the triangle is ….

Correct answer
A
Right angled triangle
B
Obtuse angled triangle
C
Equilateral triangle
D
Acute angled triangle

Solution

Key Idea Use sine rule, i.e.

\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}

Given,

s i n B s i n C = \frac{b c}{a^{2}}

\Rightarrow a^{2} = \frac{b c}{s i n B s i n C}

\Rightarrow a^{2} = (\frac{b}{s i n B}) (\frac{c}{s i n C})

\Rightarrow a^{2} = {(\frac{a}{s i n A})}^{2}

\Rightarrow {s i n}^{2} A = 1

\Rightarrow s i n A = 1 = s i n 90^{o}

\Rightarrow A = 90^{o}

Hence, the correct answer is option: 'A'.

In ΔABC, with the usual notations, if sinBsinC=bca2, then the triangle is ….

Solution

Relevant Questions

In $Δ A B C,$ with the usual notations, if $s i n B s i n C = \frac{b c}{a^{2}},$ then the triangle is ….