Find the angle theta to the nearest minute without using a calculator: tan theta = 1.063

Answer 1

tanT = 1.063

T = 46.74915785 degrees

that's with a calculator, to check with

whatever else you may come up with

each degree = 60 minutes

T = about 46 degrees and 45 minutes

tan45 = 1 as opposite side over adjacent side = 1

tanT=1.063 means T is slightly greater than 45 degrees

such as 1.75 degrees more: 45+1.75= 46.75 = 46 45/60 degrees = 46 degrees and 45 minutes

for small degrees, sinT = T, tanT =T and cosT = 1- (T/2)^2 = about 1

tanT =1.063 = sinT/cosT

tanT = tan(45+T) where T is a small degree angle

tan(45+T) =(tanA+tanB)/(1-tanAtanB) where A=45 and B=T

tan(45+T) = (tan45+tanT)/(1-tan45tanT) = (1+tanT)/(1-tanT)=1.063

1+tanT = 1.063 -1.063tanT

.063 = 2.063tanT

tanT =.063/2.063 =about.03= about T

45+T = 45.03 = 45 degrees and 1.8 minutes

round off to 45 degrees 2 minutes

which differs from the calculator's 46 and 45 minutes, a difference of 103 minutes, which isn't that much, just one degree and 43 minutes difference, maybe as small as the tanA=A approximation.