(B) In $\Delta ABC$, $AC = 5$ and hypotenuse $BC = 13$, with $m \angle A = 90^\circ$.By the Pythagorean theorem:$AB^2 = BC^2 - AC^2$$AB^2 = 13^2 - 5^2

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(B) In $\Delta ABC$, $AC = 5$ and hypotenuse $BC = 13$, with $m \angle A = 90^\circ$.By the Pythagorean theorem:$AB^2 = BC^2 - AC^2$$AB^2 = 13^2 - 5^2 = 169 - 25 = 144$$AB = \sqrt{144} = 12$Now, $\tan B = \frac{\text{side opposite to } \angle B}{\text{side adjacent to } \angle B} = \frac{AC}{AB} = \frac{5}{12}$.

Class 10 Mathematics Introduction to Trigonometry Mix Examples - Introduction to Trigonometry

Medium

In $\Delta ABC$, $AC = 5$, $BC = 13$, $m \angle A = 90^\circ$, then $\tan B = \ldots$

A
$\frac{5}{13}$
B
$\frac{5}{12}$
C
$\frac{12}{13}$
D
$\frac{12}{5}$

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Introduction to Trigonometry

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Mix Examples - Introduction to Trigonometry

Prove that:
If $\tan A = \frac{3}{4},$ then $\sin A \cos A = \frac{12}{25}$

Medium

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$\frac{1}{\sin ^{2} \theta}-1 = \ldots \ldots \ldots$

Easy

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If $\operatorname{cosec} \theta = \frac{2}{\sqrt{3}}$,then $\theta = \ldots$ (in $^\circ$)

Easy

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If $\cos 9 \alpha = \sin \alpha$ and $9 \alpha < 90^{\circ},$ then the value of $\tan 5 \alpha$ is

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Which of the following pairs is correct for trigonometric inter-relationships?

$1. \cos \theta$ $a. \frac{\cos \theta}{\sin \theta}$

$2. \tan \theta$ $b. \frac{1}{\csc \theta}$

$3. \cot \theta$ $c. \frac{1}{\sec \theta}$

$4. \sin \theta$ $d. \frac{1}{\cot \theta}$

$e. \sin \theta \cdot \cos \theta$

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$1. \cos \theta$	$a. \frac{\cos \theta}{\sin \theta}$
$2. \tan \theta$	$b. \frac{1}{\csc \theta}$
$3. \cot \theta$	$c. \frac{1}{\sec \theta}$
$4. \sin \theta$	$d. \frac{1}{\cot \theta}$
	$e. \sin \theta \cdot \cos \theta$

In $\Delta ABC$, $AC = 5$, $BC = 13$, $m \angle A = 90^\circ$, then $\tan B = \ldots$

Similar Questions

Prove that:If $\tan A = \frac{3}{4},$ then $\sin A \cos A = \frac{12}{25}$

$\frac{1}{\sin ^{2} \theta}-1 = \ldots \ldots \ldots$

If $\operatorname{cosec} \theta = \frac{2}{\sqrt{3}}$,then $\theta = \ldots$ (in $^\circ$)

If $\cos 9 \alpha = \sin \alpha$ and $9 \alpha < 90^{\circ},$ then the value of $\tan 5 \alpha$ is

Which of the following pairs is correct for trigonometric inter-relationships? $1. \cos \theta$ $a. \frac{\cos \theta}{\sin \theta}$ $2. \tan \theta$ $b. \frac{1}{\csc \theta}$ $3. \cot \theta$ $c. \frac{1}{\sec \theta}$ $4. \sin \theta$ $d. \frac{1}{\cot \theta}$ $e. \sin \theta \cdot \cos \theta$

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Prove that:
If $\tan A = \frac{3}{4},$ then $\sin A \cos A = \frac{12}{25}$