Question

In the figure above, GK is a diameter of circle N, GN and NK are radii, m∠D=60º and m∠F=60º. Find the measure of each of the numbered angles

Answer 1

here are some points that might help
1.
A point lies 30 feet from the base of a tree. The angle of elevation from the point to the top of the tree is 25°. Find the height of the tree.

13.7 feet 14.0 feet
27.6 feet

2.
A tower stands at a height of 45 meters. A point lies 12 meters from the base of the lighthouse. Find the angle of elevation.

75º 60º
15º

3. An airplane takes off with an angle of elevation of 25º. It flies 1,100 feet before the angle levels off. What is the plane's altitude at this point? 997 ft 465 ft
513 ft

4. The odometer on a car lets us know when the car is running out of gas. The pointer on the odometer is 6 cm long. When the angle of elevation of the pointer is 32°, the car is low on gas. Find the height of the tip of the odometer when the car is low on gas. 5 cm 32 cm
3.2 cm

5.
Given m∠ABC=90°. If AD=4 cm and DC=16 cm, find BA, BD and BC.

8 cm; 7 cm; 4√5 cm 4√5 cm; 8 cm; 8√5 cm
8 cm; 7 cm; 8√5 cm

6.
If a=35 cm and c=37 cm, find b.

2 cm 36 cm
12 cm

7. In a 30-60-90 triangle, the shorter leg has length of 8√3 m. Find the length of the other leg (L) and the hypotenuse (H). L=16√3 m; H=24√33 m L=24 m; H=16√3 m
L=4√3 m; H=24 m

8. Tan x=1.8040. Find x. 61º 29º
34º

9.
In a right triangle, the hypotenuse, c, has a length of 15 inches and m∠A=37°. Find a and b.

a=9 in; b=12 in a=3 in; b=9 in
a=12 in; b=3 in

10.
Write the ratio in terms of sine, cosine or tangent: b/12

tan 30 cos 30
sin 30

11.
Find the radius of circle E.

AE, EB, and EC AE, EB, and DC
AC, DC, and EB

12.
The diameter of the smaller circle is 3 m and the diameter of the larger circle is 4 m. If KL=3 m, find LM.

1 m 1.5. m
2 m

13.
In circle Q, RS is a ___.

Tangent Diameter
Chord

14.
QS=1/2___

QT US
RS

15.
QT=___=___.

UQ and QS QS and US
US and RS

16. Circle A has a radius of 3 m. What is the length of the longest chord in circle A? 3 m 9 m
6 m

17. The longest chord of a circle is 12 m. Find the radius of the circle. 12 m 9 m
6 m

18. The longest chord of a circle is 4x. Find the radius of the circle. 4 2x
x

19.
A cat is watching a bird fly overhead from the ground. The cat's line of sight is 67 feet, and the bird is 22 feet from the ground. What is the bird's angle of elevation?

19º 21º
23º

20.
A scuba diver is on the ocean floor and looking up at his boat on the surface of the ocean. The diver is 38 meters under water, and 5000 meters from the boat. What is the boat's angle of depression?

0.44º 4.5º
0.3º

21.
The congruent sides, GL and LK of a gable roof are shown. What is the length of GK, the span of the roof?

55.2 feet 57.5 feet
60.6 feet

22. What is the radius of a circle in which the longest chord has length 12? 2 4
6

23. What is the radius of a circle in which the longest chord has length 15.24? 7.62 15.24
30.48

24. What is the radius of a circle in which the longest chord has length 9? 9 4.5
2.25

25. What is the radius of a circle in which the longest chord has length y? 2y y
1/2 y

26. What is the radius of a circle in which the longest chord is 10 m? 5 m 10 m
20 m

27.
A tree that is 74 feet tall casts a 69 foot shadow. What is the measure of the angle of elevation of the sun?

47º 55º
70º

28. A man is standing on the corner, and he casts a shadow of 8.5 feet. The angle of elevation of the sun is 35º. How tall is the man? 8.5 feet 5.9 feet
6.2 feet

29. A gravestone that is 3 feet tall casts a shadow of 4.5 feet on the ground. What is the angle of elevation of the sun? 33.69º 45.5º
66º

Part 2

Short Answer: Type your response in the text box below each item. If necessary, spell out mathematical symbols. (Each question is worth five points)
30.
In the figure above, GK is a diameter of circle N, GN and NK are radii, m∠D=60º and m∠F=60º. Find the measure of each of the numbered angles.


31.
In the circle shown, express the ratio 18/19 as the sine, cosine or tangent of an angle measure. Find x to the nearest degree.


32.
Given circle G above:

1. Name the center of the circle

2. Name two radii of the circle

3. Name a diameter of the circle

4. Name three chords of the circle

5. Name a tangent to the circle

6. Name a secant to the circle

Answer 2

CAN I GET THE ANSWER TO THOSE PLEASE