Pythagorean Theorem
Triangle JKL is a 30-60-90 degree right triangle with side length LK = 4 and measure of angle J = 30 degrees. Use the Pythagorean Theorem to find the length of the third side: Refer to p. 360.
4 sqrt 3
What's one positive reference angle of 90 degrees?
450 degrees
A fire truck has an 84 ft. ladder extended against a building forming a 55-degree angle with the top of the truck. The truck is 8ft. tall. The firefighters are trying to reach a window that is 75 ft. tall above the ground. Will they be able to reach the window using the ladder set at the angle?
76.8 ft
The angles given are in standard position. What is the reference angle for each given angle? Refer to page 373. 6. 65 degrees 7. 145 degrees
6. 65 degrees
7. 35 degrees
Given the right triangle below, write the 6 trig ratios for the given angle with measure theta. a = 20 o = 21 h = 29
sin = 21/29 csc = 29/21
cos = 20/29 sec = 29/20
tan = 21/20 cot = 20/21
Use the Pythagorean Theorem to find the hypotenuse. Refer to Example 2) Step 2) p. 358
17
What's a positive reference angle of pi/2?
5pi/2
A clock has a minute hand only which had a length of 8cm. If it starts in the 12 o'clock position as pictured, write the function rule describing the distance, d, of the tip of the minute hand from the horizontal diameter of the clock after "t" minutes.
pi/30
In what quadrant does the angle, given in radians, lie? Refer p. 373. 8. pi/6 9. 5pi/3
8. Q1
9. Q4
A 45-45-90 triangle with side length OM = 2. What are the 6 trig ratios for angle N with measure theta? a = 2 o = 2 h = 2 sqrt 2 (Simplify)
sin = 1/ sqrt 2 csc = sqrt 2
cos = 1/sqrt 2 sec = sqrt 2
tan = 1 cot = 1
The lengths of the legs are 4 and 4 sqrt 3 units. ?Use the Pythagorean Theorem to find the hypotenuse. Refer to p. 366.
8
Identify one positive and one negative reference angle of 540 degrees.
900 degrees
-180 degrees
A closed umbrella casts a shadow when the sun shines at a 16.3° angle to the ground. How tall is the top of the umbrella to the nearest foot?
7
What is the negative angle of rotation for the angle with given positive angle of rotation? Refer to p. 373. 10. pi/6 11. 110 degrees
10. -90 degrees
11. -250 degrees
A tree casts a shadow with the ground creating a right triangle. The angle the sun makes with the top of the tree is 49 degrees. What is the angle that the sun makes with the shadow if the tree trunk makes a 90-degree angle with the ground?
41 degrees
Triangle MNO is a 45-45-90 degree triangle with side length OM = 2. Find the hypotenuse using the Pythagorean: Example 4) Refer to p. 360.
2 sqrt 2
Identify one positive and one negative reference angle of pi/2.
5pi/2
-3pi/2
The sun shines at a 75° angle to the ground. How long is the shadow cast by a 15 ft tall cactus? Round to the nearest foot. Refer to p. 363.
4
Convert each radian measure to a degree measure. Refer to p. 373. 12. pi/3 13. 7pi/4
12. 60 degrees
13. 315 degrees
An entrance ramp to the interstate makes the 17-degree angle with the street. What is the measure of the angle that the ramp makes with the interstate?
73 degrees
Find the unknown side length. Use the Pythagorean Theorem. a = 5 c = 13
12
Identify both positive and negative reference angles of 90 degrees. Radians and degrees.
5pi/2
450 degrees
Roshaun sees two rock formations on the other side of a canyon from where he is hiking. One is directly across the canyon, and the other is across at an angle of 27°. How far apart are the two rock formations? Round your answer to the nearest tenth. Refer to p. 364.
94
Convert each degree measure to a radian measure. Refer to p. 373. 14. -13 degrees 15. 480 degrees
14. -pi/6 or 11pi/6
15. 8pi/3
Titus is standing on the bank of a river. Koko is on a bridge that makes a right triangle to Titus and the river. Titus looks up at a 33.5-degree angle. What is the angle that is created by Koko looking down at Titus?
56.5 degrees