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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
Statement A (Assertion) : In a $\triangle A B C$, right angled at $B$, if $\sin A=\frac{8}{17}$, then coss $A=\frac{15}{17}$ and $\tan A=\frac{8}{15}$.
Statement R (Reason) : For acute angle 0 , $\cos \theta=\frac{\text { Hypotenuse }}{\text { Base }}$ and $\tan \theta=\frac{\text { Base }}{\text { Perpendicular }}$.
  • A
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
  • B
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
  • ✓
    Assertion $(A)$ is true but reason $(R)$ is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
✓

Answer

Correct option: C.
Assertion $(A)$ is true but reason $(R)$ is false.
(c) : Clearly, reason is false.
Given, $\sin \lambda=\frac{8}{17}$
$
\cos A=\sqrt{1-\left(\frac{8}{17}\right)^2}=\sqrt{\frac{289-64}{17^2}}=\frac{15}{17}
$
$
\tan A=\frac{\sin A}{\cos A}=\frac{8 / 17}{15 / 17}=\frac{8}{15}
$
$\therefore$ Asecrtion is true.

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