It is given that α is anacute angle and that tan α = #sqrt(5)/"2"# . Answer the follwoing question!?

It is given that α is an acute angle and that tan α = #sqrt(5)/"2"#

(a) Draw a right-angled triangle showing this information.

(b) Use Pythagoras’ theorem to find the length of the unknown side.

(c) Hence:
(i) write down the exact values of sin α and cos α,

(ii) show that #sin^2α + cos^2α = 1#

1 Answer
Mar 27, 2018

Please see below.

Explanation:

.

#color(red)((a))#

#tanalpha=("Opposite")/("Adjacent")=sqrt5/2#
enter image source here

#color(red)((b))#

#(BC)^2=(AB)^2+(AC)^2#

#(BC)^2=2^2+(sqrt5)^2=4+5=9#

#BC=sqrt9=3#

#color(red)((c))#

#color(red)((i))#

#sinalpha=("Opposite")/("Hypotenuse")=sqrt5/3#

#cosalpha=("Adjacent")/("Hypotenuse")=2/3#

#color(red)((ii))#

#sin^2alpha=(sqrt5/3)^2=5/9#

#cos^2alpha=(2/3)^2=4/9#

#sin^2alpha+cos^2alpha=5/9+4/9=9/9=1#