Download Homework p. 782-785: 2,5,6,8a,c,13-15,19,22,30,32,38,41,43,48,55

14-3 RIGHT TRIANGLES AND TRIGONOMETRIC RATIOS (p. 778-785)
Do the Investigation: Right Triangle Ratios on p. 778. Perhaps only draw two right
triangles, one for each partner (to save time).
The trigonometric ratios for a right triangle are the six different ratios of the sides of a
right triangle. These ratios do not depend on the size of the right triangle. They depend
only on the size of the acute angles in the triangle.
Sketch a right triangle with right angle C and acute angles A and B. Label the side
lengths a, b, and c.
In a right triangle that has an acute A , the ratios are defined as follows.
sin A 
opposite leg a

hypotenuse
c
cos A 
adjacent leg b

hypotenuse
c
tan A 
opposite leg a

adjacent leg b
csc A 
1
hypotenuse
c


sin A opposite leg a
sec A 
1
hypotenuse
c


cos A adjacent leg b
cot A 
1
adjacent leg b


tan A opposite leg a
Discuss the meaning of SOHCAHTOA and Oscar Had a Heap of Apples as ways to
remember the definitions of sin, cos, and tan.
Example: A tourist visiting Washington, DC is seated on the grass and is looking up at
the top of the Washington Monument which is 555 feet tall. The angle of her line of
sight with the ground is 27  . Find her distance from the base of the monument. Make an
accurate sketch and make sure that you are in degree mode.
Do 1 on p. 779. Find AB (the length of the lateral edge) in the above right triangle.
7
. Find the sin P, tan P, and
25
cos Q in fraction and in decimal form. Make a sketch, use the Pythagorean Theorem to
find the third side of the triangle, and calculate the ratios.
Example: In PQR, R is a right angle and cos P 
Do 2 on p. 780.
Example: A man 6 feet tall is standing 50 feet from a tree. When he looks at the top of
the tree, the angle of elevation is 42 . Find the height of the tree to the nearest foot.
Make a sketch.
Ans.: 51 ft.
Do 3b on p. 780.
To find the measure of an acute angle in a right triangle, you can use the inverses of the
trigonometric functions: sin -1 , cos -1 , or tan -1 .
Example: In KMN, N is a right angle, m = 7, and n = 25. Find the measure of K
to the nearest tenth of a degree.
Do 4a and b on p. 781.
Example: A straight road that goes up a hill is 800 feet higher at the top than at the
bottom. The horizontal distance covered is 6515 feet. To the nearest degree, what angle
does the road make with level ground?
Do 5 on p. 781.
Homework p. 782-785: 2,5,6,8a,c,13-15,19,22,30,32,38,41,43,48,55,56,64
13-15. Also consider angles in quadrants other than quadrant .
41. Use tan -1 (
150
)
210
43. Use the tan ratio twice to find both segments of the base.
48a. 90 2  60.5  67 ft.
6
)  3.4 
b. Use tan -1 (
100