Answer

Verified

413.4k+ views

**Hint:**The problem can be solved by constructing a right angled triangle and using the sine of the angle formula, between the base and the hypotenuse to calculate the required ratio of the sides.

**Complete step by step solution:**Given below shows the right angle triangle ABC.

ABC is aright angled triangle, right angled at C. The side AC is the base which is a horizontal side. AB is t called the hypotenuse, which is the inclined and longest side of the triangle while the side BC is called the altitude or perpendicular side of the triangle. The perpendicular is the shortest side of a right angled triangle.

The important thing related to any right angled triangle is that Pythagoras theorem is applicable. It is a theorem that relates the three sides of a right angled triangle. According to the theorem, the square of the hypotenuse is equal to the square of the base plus the square of the perpendicular.

In right angled triangle ABC, applying Pythagoras theorem

$A{B^2} = B{C^2} + A{C^2}$

${H^2} = {B^2} + {P^2}$

$H = \sqrt {{B^2} + {P^2}} $

In the right angled triangle, sine of the angle is the ratio of the side which is opposite to the angle to the hypotenuse.

$

A{B^2} = B{C^2} + A{C^2} \\

AB = \sqrt {B{C^2} + A{C^2}} \cdots (1) \\

$

The sine of angle A is given by,

$

\sin A = \dfrac{P}{H} \\

\sin A = \dfrac{{AC}}{{AB}} \cdots (2) \\

$

Substituting the value of AB in equation (2)

$\sin A = \dfrac{{AC}}{{\sqrt {B{C^2} + A{C^2}} }}$

**Note:**The important steps are

(i) The use of Pythagoras theorem for the evaluation of hypotenuse in terms of base and perpendicular.

(ii) The sine of the angle is the ratio of the opposite side of the angle to the hypotenuse.

Recently Updated Pages

How do you find slope point slope slope intercept standard class 12 maths CBSE

How do you find B1 We know that B2B+2I3 class 12 maths CBSE

How do you integrate int dfracxsqrt x2 + 9 dx class 12 maths CBSE

How do you integrate int left dfracx2 1x + 1 right class 12 maths CBSE

How do you find the critical points of yx2sin x on class 12 maths CBSE

How do you find the general solution to dfracdydx class 12 maths CBSE

Trending doubts

The provincial president of the constituent assembly class 11 social science CBSE

Gersoppa waterfall is located in AGuyana BUganda C class 9 social science CBSE

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

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The hundru falls is in A Chota Nagpur Plateau B Calcutta class 8 social science CBSE

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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