Transcript Trigonometric Ratios in Right Triangles

Section 4.10
SOH – CAH - TOA
opp
hyp
θ
adj
 Degrees
> minutes > seconds
There are 60 minutes in a degree (noted’)
3600 seconds in a degree (noted ”)
Ex. 57°34’15’’
57 + 34/60 + 15/3600
57 + .567 + .0041
57.5711°
 Suppose
that the distance from the top
of a balcony to the edge of the pool is
86 feet. The view from the balcony to
the edge of the pool forms an angle of
60° along the horizon. How high above
the ground is the balcony?
x
sin 60 
86 feet
86 feet
74 feet
60°
pool
A
beam supporting a roof is slanted at an
angle of 38° from the horizontal. If the
horizontal distance under the beam is 4.6
meters, how long is the beam?
4.6
cos 38 
x
38°
4.8
X = 5.8 feet
 To
the nearest tenth of a degree, give the
measures of the angles in a right triangle
whose sides have the given measures:
11, 60, 61
11
sin x 
61
60
10.4
61
90 + 10.4 + y = 180°
y = 79.6°
11
 Find
6
2
the measure
of the acute angle
formed by the line
with equation
y = 3x and the x –
axis.
6
tan x 
2
X = 71.57°
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