Introduction To Trigonometric Ratios Page 3
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2
3Finding The Angle If You Know at Least Two Sides
If you know two of the sides and want to find the angle, you need to use the inverse
functions (sin
-1
/cos
-1
/tan
-1
). On the calculator, press the 2
nd
key and then the trig function
key needed. Enter the ratio of the two sides and hit enter.
Ratio:
Angle (use the inverse functions)
tanX = 1
then X =tan
-1
(1) = or 2nd tan (1) on the calculator = 45º
sinX = 0.8660
X= sin
-1
(0.8660) = 60º
cosX = 0.7986
X= cos
-1
(0.7986) = 37º
tanX = 5/7
X= tan
-1
(5/7) = 35.5º
So you can use this in a triangle:
sin ( x) = 12/13
so: sin
-1
(12/13) = x = 67.4º
3
tan(x) = 3/4
12
13
so: tan
-1
(3/4) = x
x = 36.9º
xº
xº
4
Don’t forget you can use the Pythagorean Theorem to find the third side!
Try to find the missing values:
roof pitch is 7:12
?
5’
?
?º
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