Introduction to Trigonometry: CBSE Class 10 Mathematics practice questions

C. three, sides, measure

Tri = three, gon = sides and metron = measure, so trigonometry literally means "measuring three-sided figures". It studies the relationships between the sides and angles of a triangle, which is exactly what lets us find the height of the tower from the distance and the angle of sight.

D. $\dfrac{9}{41}$

The side opposite $\angle C$ is $AB = 9$, so $\sin C = \dfrac{AB}{AC} = \dfrac{9}{41}$. The trap is to reuse the answer for $\angle A$: $\dfrac{40}{41}$ is $\sin A$ (which is also $\cos C$). $\dfrac{9}{40}$ is $\tan C$ and $\dfrac{41}{9}$ is $\operatorname{cosec} C$.

D. $\dfrac{60}{61}$

$(1+PQ)^2 = 11^2 + PQ^2$ gives $1 + 2PQ = 121$, so $PQ = 60$ cm and $OQ = 61$ cm. Then $\cos Q = \dfrac{PQ}{OQ} = \dfrac{60}{61}$. $\dfrac{11}{61}$ is $\sin Q$. Using $OP$ instead of $OP^2$ gives $PQ=5$ and the false $\dfrac56$, and $\dfrac{61}{62}$ comes from taking the hypotenuse $61$ as $PQ$ and then adding $1$ again for $OQ$.