Answer

Verified

388.8k+ views

**Hint:**In this problem we have to calculate the values of six trigonometric ratios for a given right angled triangle. First, we will draw a diagram of the given right angled triangle with all the data we have. We need to represent all the data like side lengths, angels we have in the given problem. Now we will consider the two vertices other than the right angled vertex and we will write the adjacent, opposite ide to the respective vertex. Now we will use the basic definitions of the trigonometric ratios and calculate the values of the trigonometric ratios for both the vertices in the triangle.

**Complete step-by-step solution:**

Given that, $ABC$ is a right-angle triangle with right angle at $C$. Hence the triangle $ABC$ is represented as

Now we have the values of side lengths of the above triangle as $a=20$, $b=21$, $c=29$. Now the above triangle is represented as

In the above triangle the hypotenuse is $AB=c=29$

Now considering the angle $\angle BAC$ in the above triangle. Adjacent side to the angle $\angle BAC$ is $AC=b=21$, Opposite side to the angle $\angle BAC$ is $BC=a=20$.

From the basic definitions of the trigonometric ratios, we have the values of all trigonometric ratios as

$\sin A=\dfrac{\text{Opposite side}\left( a \right)}{\text{Hypotenuse}\left( c \right)}=\dfrac{20}{29}$,

$\cos A=\dfrac{\text{Adjacent side}\left( b \right)}{\text{Hypotenuse}\left( c \right)}=\dfrac{21}{29}$,

$\tan A=\dfrac{\text{Opposite side}\left( a \right)}{\text{Adjacent side}\left( b \right)}=\dfrac{20}{21}$,

$\cot A=\dfrac{\text{Adjacent side}\left( b \right)}{\text{Opposite side}\left( a \right)}=\dfrac{21}{20}$,

$\sec A=\dfrac{\text{Hypotenuse}\left( c \right)}{\text{Adjacent side}\left( b \right)}=\dfrac{29}{21}$,

$\csc A=\dfrac{\text{Hypotenuse}\left( c \right)}{\text{Opposite side}\left( a \right)}=\dfrac{29}{20}$.

Now considering the angle $\angle ABC$ in the above triangle. Adjacent side to the angle $\angle ABC$ is $BC=a=20$, Opposite side to the angle $\angle ABC$ is $AC=b=21$.

From the basic definitions of the trigonometric ratios, we have the values of all trigonometric ratios as

$\sin B=\dfrac{\text{Opposite side}\left( b \right)}{\text{Hypotenuse}\left( c \right)}=\dfrac{21}{29}$,

$\cos B=\dfrac{\text{Adjacent side}\left( a \right)}{\text{Hypotenuse}\left( c \right)}=\dfrac{20}{29}$,

$\tan B=\dfrac{\text{Opposite side}\left( b \right)}{\text{Adjacent side}\left( a \right)}=\dfrac{21}{20}$,

$\cot B=\dfrac{\text{Adjacent side}\left( a \right)}{\text{Opposite side}\left( b \right)}=\dfrac{20}{21}$,

$\sec B=\dfrac{\text{Hypotenuse}\left( c \right)}{\text{Adjacent side}\left( a \right)}=\dfrac{29}{20}$,

$\csc B=\dfrac{\text{Hypotenuse}\left( c \right)}{\text{Opposite side}\left( b \right)}=\dfrac{29}{21}$.

**Note:**In this problem we have a lot of data related to triangles. So, it is easy to solve when we have the diagrammatic representation of the given data. Without representing the given triangle, it will be very hard to solve the problem.

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Change the following sentences into negative and interrogative class 10 english CBSE