find the measure of angle A if...?

Question

in triangle ABF, F is the right angle. AB=8, BF=5,AF=6.245. how do i find the measure of angle A two different ways?

Answer 1

You could use either sine, cosine or tangent depending on which two sides you choose (since all three are given).

sineA = opposite leg/hypotenuse = 5/8

cosine A = adjacent leg/hyp. = 6.245/8

Use inverse sine and cosine to get the measure of A.

Answer 2

angle A = arccos 6.245/8 = 38.68217 degrees.
angle A = arctan 5/6.245 = 38.68217 degrees
angle A = arcsin 5/8 =38.68218 degrees

Answer 3

method 1: use simple trigonometry (either sin, cos or tan)
sin A = opposite / hypotenuse
A = arcsin (5/8)

A = 0.675 radians (38.7 degrees)

method 2: use cosine rule (or sine rule but its the same as method 1 in this case)
a^2 = b^2 + c^2 - 2bc cos A
cos A = (b^2 + c^2 - a^2) / (2bc)
A = arccos [(b^2 + c^2 - a^2) / (2bc)]

b = 8
c = 6.425
a = 5 (as opposite angle A)

so A = arccos [(8^2 + 6.245^2 - 5^2) / (2*8*6.245)]
A = arccos[0.781]

A = 0.675 radians (38.7 degrees)

Answer 4

you can use any one of the formulae:

sine ABF= opp/hyp
sine ABF=6.245/8
sine ABF=0.780625
ABF= arcsine 0.780625
ABF=51.31783549 degrees

cos ABF= adj/hyp
cos ABF=5/8
cos ABF=0.625
ABF= arccos 0.625
ABF=51.3178 degrees

tan ABF= opp/adj
tan ABF=6.245/5
tan ABF=1.249
ABF= arctan 1.249
ABF=51.3178 degrees

Answer 5

use trigonometrical ratio(s), sinA=5/8 for example. then use tables or calculator to find the value of A.
A=38.682 degrees