Right Triangle Trigonometry Review

Trig Functions

100

What is the trigonometric ratio for cosecant?

^{hypotenuse/opposite}

200

What does SOH CAH TOA stand for?

Sine: Opposite/Hypotenuse

Cosine: Adjacent/Hypotenuse

Tangent: Opposite/Adjacent

300

If cosx=3/4, what is the value of secx?

4/3

400

If sinx=1/3, what is cosx?

2(2)^1/2/3

500

If cscx=18/9, what is the value of tanx?

(3)^1/2/3

Solving with Right Triangles

100

What is the hypotenuse length of a 45-45-90 triangle with a leg length of 5 cm?

5(2)^1/2 cm

200

What is the length of the hypotenuse of a 30-60-90 triangle if the long leg length is 9 mm?

6(3)^1/2 mm

300

If tanx=.9842, what is the angle measure of x in degrees? 

44.5 degrees

400

What is the length of the hypotenuse of a triangle given an angle of 63 degrees and its adjacent side being 12?

26.4

500

What is the angle measure (in degrees) of x given its adjacent side is 11 and its opposite side is 14?

51.8 degrees

Angles

100

Exactly how many radians are in a full rotation?

2 pi

200

Convert 54 degrees into radians 

3pi/10 or .9425 radians

300

Convert 7pi/13 into degrees

1260/13 or 96.9231 degrees

400

Find a positive and negative coterminal angle of 810 degrees

Positive: 1170, 450, 90 (just a few that would work)

Negative: -270, 

500

Find a positive and negative coterminal angle of 22pi/7

Positive: 36pi/7, 8pi/7

Negative: -6pi/7

Story Problems

100

An equilateral triangle has a side length of 14 inches. Find the length of the triangle's altitude. 

7(3)^1/2 inches

200

Susan's square garden has a perimeter of 116 feet. Find the diagonal length from the top right corner of her garden to the bottom left corner.

29(2)^1/2 feet or 41.01 feet

300

Richard is flying a kite. The kite string makes and angle of 57 degrees with the ground. If Richard is standing 100 feet from the point on the ground directly below the kite, find the length of the kite string.

183.6 feet

400

The angle of depression from the top of a cliff to the point A on the ground is 35 degrees. If point A is 280 feet from the base of the cliff, how tall is the cliff? 

196.1 feet

500

A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom. 

11.7 degrees

Arc Length/Area of a Sector

100

What are the formulas for area of a circle and circumference of a circle in terms of radius?

Area: A=pi(r)²

Circumference: C=2pi(r)

200

If the area of a circle is 64pi cm², what is the area of a sector of that same circle with a central angle of 90 degrees?

16pi cm² or 50.3 cm²

300

Find the arc length given the following information:

r=7 in, central angle=210 degrees 

49pi/6 in or 25.7 in

400

Find the arc length given the following information:

r=5 cm, central angle=3pi/10

3pi/2 cm or 4.7 cm

500

Find the area of the sector of a circle given the following information: 

r= 6cm, central angle: 3pi/4

27pi/2 cm² or 42.4 cm²