Question

In triangle ABC, right angled at B, if one angle is ${45}^o$, find the value of sin A, cos C, cot A and tan C respectively.

• A. 1,1, 1/√3, 1/√3
• B. 2,2, √2, √2
• C. 1/√2, 1/√2, 1,1
• D. 1/√3, 1/√3, 1,1

Answer 1

The correct option is C

1/√2, 1/√2, 1,1

In right angle triangle ABC, $SinA=\frac{BC}{AC},SinC=\frac{AB}{AC}$

In right angle triangle ABC
Let $\angle A={45}^o,angle\angle B={90}^o$
Then $\angle C={180}^o-{90}^o-{45}^o={45}^o$
Let AB = BC = a
Apply Pythagoras theorem in $△$ABC
$AC=\sqrt{(}{a}^2+a^2)=a\sqrt{2}$
Using Trigonometric ratio
$sinA=sin{45}^o=\frac{BC}{AC}=\frac{a}{a\sqrt{2}}=\frac{1}{\sqrt{2}}$
$cosC=cos{45}^o=\frac{BC}{AC}=\frac{a}{a\sqrt{2}}=\frac{1}{\sqrt{2}}$
$cotA=cot{45}^o=\frac{AB}{BC}=\frac{a\sqrt{2}}{a\sqrt{2}}=1$
$tanC=tan{45}^o=\frac{AB}{BC}=\frac{a\sqrt{2}}{a\sqrt{2}}=1$