What's That?
True or False?
Doing the Math I
Doing the Math II
Use Your Calculator
100
A triangle with a 90 degree angle.
A right triangle.
100
For an acute angle in a right triangle, the cosine is the ratio of the hypotenuse to the adjacent side.
False.
It is the ratio of the adjacent side to the hypotenuse.
100
Find the length of the hypotenuse. Round to 3 decimal places if necessary.
sin(30) = 5/h
h = 5/sin(30) = 10
100
Which number is larger . . . cos 56° or cos 63°?
cos 56°
Why is cos 56° larger than cos 63° when 63° is bigger than 56°?
100
Use your calculator to find the value of sin 135° correct to four decimal places.
0.7071
200
The Greek letter beta.
200
The sine, cosine, and tangent ratios can be used with obtuse triangles.
False.
The triangle must be a right triangle to use these ratios.
200
What is the tan C?
tan C = 6/8 = 3/4
200
In the 3-4-5 right triangle, find the measure of angle B to the nearest degree.
sin B = 4/5 = 0.8
Using the table of page 494 of your textbook and rounding the values to 0.8,
sin 53 ~~ 0.8 ` so angle B is about 53°`
200
Use your calculator to find cos 0.
1
300
sin 3
sin 3 ~~ 0.0523
300
Using a calculator, the value of sin 54° is approximately 0.8090.
True
300
What is the angle of elevation, x?
tan x = 300/400
tan x =.75
`after some trial and error on the calculator, the angle whose tan is 0.75 is about 36.9 degrees`
300
From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40º. If the tower is 45 feet in height, how far is the partner from the base of the tower, to the nearest tenth of a foot?
•Remember that the "angle of depression" is from a horizontal line of sight downward
• It is assumed that the tower is vertical, making it perpendicular with the ground.
• This solution will use alternate interior angles from the parallel horizontal lines, so place 40º inside the triangle by the partner (bottom right).
• This solution deals with "opposite" and "adjacent" making it a tangent problem.
300
Use your calculator to find sin 0.
0
400
cos 3
cos 3 ~~ 0.9986
400
In a right triangle, the tangent ratio of an angle has the form 
False! The tangent ratio is the reciprocal of that!
400
The anchor is on the bottom of the lake. How deep is the water under the boat? Round to two decimal places if necessary.
sin 39 = d/30
30*sin 39 = d
d ~~ 18.88 m
400
Find the shadow cast by a 10 foot lamp post when the angle of elevation of the sun is 58º. Find the length to the nearest tenth of a foot.
• Remember that the "angle of elevation" is from the horizontal ground line upward.
• It is assumed that the lamp post is vertical, making it perpendicular with the ground.
• Shadows are on the ground! If you place the "shadow" on the hypotenuse you have created an apparition ( a "ghost"), not a shadow!
• This solution deals with "opposite" and "adjacent" making it a tangent problem.
400
Use your calculator to find tan 0.
0
500
SOH CAH TOA
A mnenonic device used to help you remember which ratios go with which trig function.
Sine Opposite Hypotenuse
Cosine Adjacent Hypotenuse
Tangent Opposite Adjacent
500
In the right triangle shown, it follows that tan 45° = 1.
True. Explain.
500
A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?
Think of this problem as working with two separate triangles:
(1) the larger triangle with the 40º angle and a vertical side that represents the ENTIRE height, b, of the tower, and
(2) the smaller triangle with the 25º angle and a vertical side, a, that represents the height of the first (bottom) section of the tower.
• Solve for the vertical heights (b and a) in the two separate triangles.
• The needed height, x, of the second (top) section of the tower will be the difference between the ENTIRE height, b, and the height of the first (bottom) section, a. You will need to subtract.
• In both triangles, the solution deals with "opposite" and "adjacent" making it a tangent problem.
• Larger triangle with height b: 
• Smaller triangle with height a: 
• Difference (b - a): 73.00166791 - 40.56876626 = 32.43290165 ≈ 32 feet
500
In a right triangle,
tan alpha = 15/8
Find the value of
sin alpha
So if the the tangent is 15/8, that means that the side opposite alpha has length 15 and the adjacent side has length 8. A right triangle with legs of 15 and 8 has a hypotenuse of length
sqrt(15^2+8^2) = sqrt(289) = 17
The sine of alpha is opp/hyp. So,
sin alpha = 15/17
500
Use your calculator to find
cos 30 / sin 60
1