List of top Mathematics Questions on Trigonometry asked in Maharashtra Class X Board

An observer at a distance of 10 m from tree looks at the top of the tree, the angle of elevation is 60$^\circ$. To find the height of tree complete the activity. ($\sqrt{3} = 1.73$)

Activity :
In the figure given above, AB = h = height of tree, BC = 10 m, distance of the observer from the tree.
Angle of elevation ($\theta$) = $\angle$BCA = 60$^\circ$
tan $\theta$ = $\frac{\boxed{\phantom{AB}}}{BC}$ $\dots$ (I)
tan 60$^\circ$ = $\boxed{\phantom{\sqrt{3}}}$ $\dots$ (II)
$\frac{AB}{BC} = \sqrt{3}$ $\dots$ (From (I) and (II))
AB = BC $\times$ $\sqrt{3}$ = 10$\sqrt{3}$
AB = 10 $\times$ 1.73 = $\boxed{\phantom{17.3}}$
$\therefore$ height of the tree is $\boxed{\phantom{17.3}}$ m.

In the figure given below, find RS and PS using the information given in $\triangle$PSR.

Taking $\theta = 30^\circ$ to verify the following Trigonometric identities:
(i) $\sin^2\theta + \cos^2\theta = 1$
(ii) $1 + \tan^2\theta = \sec^2\theta$
(iii) $1 + \cot^2\theta = \csc^2\theta$

If $\sin\theta = \frac{11}{61}$, find the value of $\cos\theta$ using trigonometric identity.

Find the value of $ \sin^2 \theta + \cos^2 \theta $:

Find the value of $ \sin 0 \times \csc 0 $:

A person is standing at a distance of 50 m from a temple looking at its top. The angle of elevation is $45^\circ$. Find the height of the temple.