Question

Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal.

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The correct option is B

Explanation for correct option:

Option B:

The acute angle in the figure is $45°$

The value of $\sin \left(45°\right)=\frac{1}{\sqrt{2}}$

The value of $\cos \left(45°\right)=\frac{1}{\sqrt{2}}$

Hence, the sine and cosine ratios are equal.

Explanation for incorrect options:

Option A:

The acute angle is $40°$ and $50°$.

The value of $\sin \left(40°\right)=0.74$ and the value of $\cos \left(40°\right)=-0.66$. Therefore, the ratios are not equal.

The value of $\sin \left(50°\right)=-0.26$ and the value of $\cos \left(50°\right)=0.96$. Therefore, the ratios are not equal.

Option C:

The acute angle is $22°$ and $68°$.

The value of $\sin \left(22°\right)\approx 0.37$ and the value of $\cos \left(22°\right)\approx 0.92$. Therefore, the ratios are not equal.

The value of $\sin \left(68°\right)\approx 0.92$ and the value of $\cos \left(68°\right)\approx 0.37$. Therefore, the ratios are not equal.

Option D:

The acute angle is $30°$ and $60°$.

The value of $\sin \left(30°\right)=\frac{1}{2}$ and the value of $\cos \left(30°\right)=\frac{\sqrt{3}}{2}$. Therefore, the ratios are not equal.

The value of $\sin \left(60°\right)=\frac{\sqrt{3}}{2}$ and the value of $\cos \left(60°\right)=\frac{1}{2}$. Therefore, the ratios are not equal.

Hence, the correct answer is option B.