Question

in right angle triangle ABC,8cm,15cm and 17cm are the lengths of AB,BC and CA respectively,then find cos A and tan A​

Answer 1

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\put(7.7,2.9){\large{A}}\put(7.7,1){\large{B}}\put(10.6,1){\large{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\put(10.5,1){\line(-4,3){2.5}}\put(7.3,2){\sf{\large{8 cm}}}\put(9,0.7){\sf{\large{15 cm}}}\put(9.4,1.9){\sf{\large{17 cm}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\end{picture}$

$\rule{170}{1}$

$\underline{\bigstar\:\textsf{According to the Question :}}$

$:\implies\sf \cos A=\dfrac{Base}{Hypotenuse} \\\\\\:\implies\sf \cos A=\dfrac{AB}{AC}\\\\\\:\implies\sf \cos A= \dfrac{8 \:cm}{17\:cm}\\\\\\:\implies\underline{\boxed{\sf \cos A= \dfrac{8}{17}}}$

$\rule{170}{2}$

$:\implies\sf \tan A=\dfrac{Perpendicular}{Base} \\\\\\:\implies\sf \tan A=\dfrac{BC}{AB}\\\\\\:\implies\sf \tan A= \dfrac{15 \:cm}{8\:cm}\\\\\\:\implies\underline{\boxed{\sf \tan A= \dfrac{15}{8}}}$

Answer 2

Answer:

Given:

AB = 8cm

BC = 15cm

CA = 17cm

⇒ Sin A = Opposite/Hypotenuse = BC = 15/17

⇒ Cos A = Adjacent/Hypotenuse = AB/AC = 8/17

⇒ Tan A = Opposite/Adjacent = BC/AB = 15/8

Diagram is in Attachment!