In a , =90^ , =12cm and BC = 5cm. Find: 1. 2. cosecA 3. 4. cosecC… - Vidyadip

Question

In a $\triangle\text{ABC},\angle\text{B}=90^\circ,\angle\text{AB}=12\text{cm}$ and BC = 5cm.
Find:

$\cos\text{A}$
$\text{cosec}\text{A}$
$\cos\text{C}$
$\text{cosec}\text{C}.$

✓

Answer

In $\triangle\text{ABC},\angle\text{B}=90^\circ$
AB = 12cm and BC = 5cm
By Pythagoras theorem, we have
$\text{AC}^2=\text{AB}^2+\text{BC}^2$
$=12^2+5^2=144+25=169$
$\Rightarrow\text{AC}=13\text{cm}$

$\cos\text{A}=\frac{\text{Base}}{\text{Hypotenuse}}=\frac{\text{AB}}{\text{AC}}=\frac{12}{13}$
$\text{cosec}\text{A}=\frac{\text{Hypotenuse}}{\text{Perpendicular}}=\frac{\text{AC}}{\text{BC}}=\frac{13}{5}$
$\cos\text{C}=\frac{\text{Base}}{\text{Hypotenuse}}=\frac{\text{BC}}{\text{AC}}=\frac{5}{13}$
$\text{cosec}\text{C}=\frac{\text{Hypotenuse}}{\text{Perpendicular}}=\frac{\text{AC}}{\text{AB}}=\frac{13}{12}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Question" from Trigonometric Ratios→Trigonometric Ratios — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is Rs. 18, find the missing frequency f.

Daily pocket allowance (in Rs.)	11-13	13-15	15-17	17-19	19-21	21-23	23-25
Number of children	7	6	9	13	f	5	4

Solve the following quadratic equation:
$\Big(\frac{\text{4x}-3}{\text{2x}+1}\Big)-10\Big(\frac{\text{2x}+1}{\text{4x}-3}\Big)=3,$ $\text{x}\neq\frac{-1}{2},\ \frac{3}{4}$

Short-Answer Question:
If $\alpha$ and $\beta$ are the zeroes of a polynomial $f(x) = x^2 + x - 2$, find the value of $\Big(\frac{1}{\alpha}-\frac{1}{\beta}\Big).$

If $(\cot\theta+\tan\theta)=\text{m}$ and $(\sec\theta-\cos\theta)=\text{n},$ prove that $\big(\text{m}^2\text{n}\big)^\frac23-\big(\text{m}\text{n}^2\big)^\frac23=1.$

The difference between the sides at right angle in a right-angled triangle is $7\ cm$. The area of the triangle is $60\ cm^2$. Find its perimeter.

The $n^{th}$ term of an AP is $(3n + 5)$. Find its common difference.

Construct a $\triangle\text{ABC}$ in which $BC = 8cm, $ $\angle\text{B}=45^\circ$ and $\angle\text{C}=60^\circ.$ Construct another triangle similar to $\triangle\text{ABC}$ such that its sides are $\frac35$ of the corresponding sides of $\triangle\text{ABC}.$

The present age of a woman is 3 years more than three times the ages of her daughter. Three years hence, the woman's age will be 10 years more than twice the age of her daughter. Find their present ages.

Find the area of a trapezium whose parallel sides are 11cm and 25cm long and nonparallel sides are 15cm and 13cm.

Find the sum of first 100 even natural numbers which are divisible by 5.