Section 7.1
Solving Right Triangles
Recall: Pythagorean Theorem: a2 + b2 = c2
SOHCAHTOA and
sin  
opposite
hypotenuse
cos 
adjacent
hypotenuse
tan  
opposite
adjacent
Ex 1: Find the values of sine, cosine, and tangent for angle B
in triangle ABC with leg AC = 18 and hypotenuse AB = 33.
csc 
1
hypotenuse

sin 
opposite
cot  
1
adjacent

tan  opposite
sec 
1
hypotenuse

cos
adjacent
Example 2: In right triangle JKL with right angle K - If J =
50o and j = 12, find k and l. (provide diagram)
Example 3: A regular hexagon is inscribed in a circle with
diameter 26.6 centimeters. Find the apothem of the hexagon.
(provide diagram)
Example 4: An observer in the top of a lighthouse determines
that the angles of depression to two sailboats directly in line
with the lighthouse are 3.5o and 5.75o. If the observer is 125
feet above sea level, find the distance between the two boats.
Recall Section 5.2-5.3, (exact values of the six trigonometric
functions for all angles between 0o and 360o that are multiples
of 30o and 45o on the unit circle ).
Sometimes you may know a trigonometric value of an angle,
but not the angle itself. In this case, you can use the inverse
of a trigonometric function. The inverse of the sine function
is the arcsine relation. Note that arcsine is NOT a function.
Similarly, the inverse of cosine is arccosine, and the inverse
of tangent is arctangent. Arcsine, arccosine, and arctangent
may also be written as sin-1, cos-1, and tan-1.
Ex 5: Solve each equation.
3
sin
x

a.
2
b. cos x  
2
2
Ex 6: Evaluate each expression.
1 6
tan(tan
)
a.
11
2
cos(arcsin
)
b.
3
Ex 7: Solve each triangle, ABC described below given right
angle C. (Provide diagram)
a. A = 33o, b = 5.8
b. a = 23, c = 45
Notice that sin 30o = cos 60o and that cos 30o = sin 60o. This
shows that sine and cosine are cofunctions.
Cofunctions:
sin θ=cos (90o – θ)
tan θ=cot (90o – θ)
sec θ=csc (90o – θ)
cos θ=sin (90o – θ)
cot θ=tan (90o – θ)
csc θ=sec (90o – θ)