Question

1) Find the value of each trig ratio. Leave as an exact answer.

) tan (A)
b) sin(X)
A
34
16
30
B
N
20
16
X
12
c) cos(C)
27
B
45
36
A

Answer 1

`\tan(a) = (opp)/(adj) \\ = (30)/(16) \\ = (15)/(8) \\ = 1.875`

`\sin(x) = (opp)/(hyp) \\ = (16)/(20) \\ = (4)/(5) \\ = 0.8`

`\cos(c) = (adj)/(hyp) \\ = (27)/(45) \\ = (3)/(5) \\ 0.6`

Explanation:

here's a very easy method to Remember your trig ratios

Ohh Hell Another Hour Of Algebra

•The first letters of the two words "Ohh Hell" represent the trig ratio for sine which is given by

`(side \: opp \: angle)/(hypotenuse)`

thus O/H

•The following first letters of the next two words "Another Hour" represent the trig ratio for cos which is the

`(adjuscent)/(hypotenuse)`

thus A/H

•The first letters of the last two words "Of Algebra" represent the trig ratio for tan which is

`(opposite \: side)/(adjuscent)`

thus O/A

if you struggle to remember which is which just follow the order on your calculator, it should guide you on which trig ratio belongs to which two letters.

NOTE: THE ADJUSCENT SIDE IS THE SIDE BETWEEN THE ANGLE AND THE THE RIGHT ANGLE (90°)

: THE HYPOTENUSE IS THE SIDE THAT IS ALWAYS OPPOSITE THE RIGHT ANGLE

To find tanA we need the side opposite angle  which is 30 units and the adjuscent side relative to angle  which is 16 units. Divide 30 by 16 to get the value of TanÂ

To find sinX we need the side opposite angle X which is 16 and the hypotenuse of the triangle which is the side opposite the right angle which is 20. Divide 16 by 20 to get the value of SinX

To find cosC, we need the adjuscent side relative to angle C which is 27 and the hypotenuse which is 45. Divide 27 by 45 to get the value of cosC.

Answer 2

answer:

1-(a). formula of TAN is perpendicular/base
A is the acute angle, that means it’s the base
tan A= 30/16
A= TAN(-1) or (tan inverse) (1.875)
A= 61.9

(b)- to find SIN (X) the same method will be used, the formula for SIN is perpendicular/hypotenuse

sin X= 16/20
X= sin(-1) (0.8)
X= 53.1



(c)- COS (C)
the formula for COS is BASE / HYPOTENUSE
cos C= 27/45
C= cos(-1) (0.6)
C= 53.1
again, i’m not sure if these are the right answers because they haven’t started the acute angle properly, but they have given the alphabet so we assumed that it’s was the acute angle, hope this helps!