Answer:
23/26 = 0.8846=0.88 [ to the nearest hundredth]
Explanation:
4 sec a-5 = 0; seca=1/cos a
Therefore;
4 sec a-5 = 0=>4/cos a - 5 = 0
Multiplying through by cos a, we have;
4-5cosa= 0=>4= 5cosa
4/5 = cosa
a = cos^{-1}0.8
=36.88
Alternatively Cos a =4/5
Sina = 3/5; {note Cos a = adjacent / hypothesis and from Pythagoras rule we can derive the value of the opposite side which is;
5^2 -4^2 = 25-16 = 9; hence the opposite side is √9 = 3;sin a = opposite/ hypothenus = 3/5}
Substituting the value of Cosa and Sina into the expression below;
2 cos a + 5 sin a ÷ 2 sin a + 5 cos a
We have ;
[2×4/5 + 5× 3/5 ]/ [2 × 3/5 + 5× 4/5]
[8/5 + 15/5 ]/ [6/5 + 20/5]
[23/5]/[26/5] = 23/5 × 5/26 = 23/26
=