Question

In triangle ABC right angled at c AC =4cm and ab=8cm find angle a and b

Answer 1

AnswEr:-

❀ Your Answer Is:-

• <A = 60°
• <B = 30°

ExplanaTion:-

Given:-

• A right angle triangle ABC right angled at C.

• AB = 8 cm.

• AC = 4 cm.

See the figure below:-

$\setlength{\unitlength}{20} \begin{picture}( 0 , 0 ) \put( 1 , 1){ \line( 0 , 1){4}}\put( 1 , 1){ \line( 1 , 0){4}}\put( 5 , 1){ \line( 0 , 1){0}}\put( 1 , 5){ \line( 1 , - 1){4}}\put(0.5, ){ \rm{C} } \put(0.5,5 ){ \rm{A} }\put(5.2, ){ \rm{B} }\put(0, 2.5){ \rm{4 \:cm} } \put(3.2, 3){ \rm{8 \: cm} } \end{picture}$

To Find:-

• The measure of <A and <B.

Concepts Used:-

$\\ \tt \bullet \: \: \sin \theta = \dfrac{P}{H} . \\ \\ \rm and \\ \\ \tt \bullet \: \: \cos \theta = \frac{B}{H} .$

Where,

• P = Perpendicular.
• B = Base.
• H = Hypotenuse.
• $\tt\theta$ = Angle.

IDs Used:-

$\rm\bullet \: \: value \: \: of \: \: \tt\sin30 \degree = \dfrac{1}{2}...id \: \: 1. \\ \\ \rm and \\ \\ \rm \bullet \: \: value \: \: of \: \: \tt \cos60 \degree = \dfrac{1}{2}...id \: \: 2.$

So Here,

• For Angle B,

• P = AC = 4 cm.
• B = BC.
• H = AB = 8 cm.

• For Angle A,

• P = BC.
• B = AC = 4 cm.
• H = AB = 8 cm.

Therefore by using IDs we get:-

$\\ \tt\mapsto \sin B = \frac{P}{H} . \\ \\ \tt\mapsto \sin B = \cancel\frac{4 \: cm}{8 \: cm} . \\ \\ \tt\mapsto \sin B = \frac{1}{2} \\ \\ \tt\mapsto \angle B = 30 \degree \\ \\ \rm(by \: \: using \: \: id \: \: 1). \\ \\ \rm similarly \\ \\ \tt\mapsto \cos A = \frac{B}{H} . \\ \\ \tt\mapsto \cos A = \cancel\frac{4 \: cm}{8 \: cm} . \\ \\ \tt\mapsto \cos A = \frac{1}{2} . \\ \\ \tt\mapsto \angle A = 60 \degree \\ \\ \rm(by \: \: using \: \: id \: \: 2).$

❝$\large\bf{\therefore}$ The Measure of angle A is 60° and measure of angle B is 30°.❞