Reviewer for Math 9

The 4th periodical exam is fast approaching. As you prepare for the exams, here are some questions which might help you in your review:

1) What ratio can be formed showing the relationship of the sides of a 30-60-90 triangle? How about a 45-45-90 triangle?

2) If the longer side of a 30-60-90 triangle is b, what ratio can be formed from this triangle?

3) If one of the congruent sides of a 45-45-90 triangle is 10 cm, what is the length of the hypotenuse?

4) How is the sine ratio of any acute angle in a right triangle defined? How about the cosine and tangent ratios?

5) How are the angles of depression and elevation drawn?

6) If the angle of elevation from a boat 765 m from the coastline to the top of a building on the coastline is 22 degrees, how high is the building?

7) A pilot, flying at an altitude of 957 ft. , sees the end of an island at angle of depression of 35 degrees. What equation can be used to solve for the distance through the line of sight of the pilot?

8) At a certain time of the day, the angle of elevation of the sun is 57 degrees. Find the height of the tree if its shadow length is 45 feet. What is the distance from the top of the tree to the point in the ground made by the shadow?

9) An industrial ladder is 35 feet long and has its base in the street. The ladder makes an angle of 30 degrees with the street when its top rests on the roof of a building on one side of the street, and it makes an angle of 25 degrees when its top rests on the roof of the building on the other side of the street. a) What equation should you use to find the height of one building? b) To find the width of the street, what terms should you add? (Hint: Find a working equation first.)

10) If two circles are congruent, what can be said about chords that are in the same area of each circle? What can you say about the radii of each circle?

11) If two secants intersect in the exterior of a circle, how will you solve for the measure of the angle formed by these secants? If you are given the measure of the angle and the smaller arc, how will you solve for the measure of the bigger arc?

12) What can you say about the relationship between the measure of an inscribed angle and its intercepted arc?

13) If two chords intersect in the interior of the circle, what can be said about the relationship of the products of each chords' segments?

14) What other segments are related to the diameter of the circle?

15) Define each of the following terms:
a) tangent
b) secant
c) chord
d) diameter
e) common tangents
f) externally tangent circles
g) internally tangent circles

16) A 30-ft ladder is used to climb a building. What height will the ladder reach if it is inclined with the ground at an angle of: (a) 30 degrees, (b) 52 degrees, and (c) 75 degrees?

17) If the radius of a circle is drawn perpendicular to a chord, what does this radius do to the chord and to the arc subtended by this chord?

18) The measure of an inscribed angle is 50 degrees. What is the measure of its intercepted arc?

19) What is the difference between a major arc and a minor arc?

20) A tangent and a secant intersect at the point of tangency. What can be said about the relationship between the inscribed angle formed and its intercepted arc?

21) What are concentric circles? How about congruent circles?

22) Can concentric circles have congruent radii?

23) A central angle measures 43 degrees. What is the measure of the arc subtended by this angle?

24) One side of a right triangle measures 10 cm. If the hypotenuse measures 15 cm, what equation can be used to measure the angle opposite the given side?

25) What is the value of sin 30? Is this value the same for all triangles with a 30-degree angle?

Answer this reviewer within 30 minutes and practice. The best way to remember the application of the different theorems we learned is to practice them. Just a question for thought: How do you make a pencil sharp?

God Bless!!!