Unit 2: Right Triangle Relationships Review
30-60-90 Triangles
· The length of the shorter leg is s
· The length of the longer leg is
· The length of the hypotenuse is 2s
45-45-90 Triangles
· The length of each leg is s.
· The length of the hypotenuse is
Soh Cah Toa or “Oscar has a heap of apples”.
The 2 acute angles of any right triangle are complementary. (add up to 90 °)
In a right triangle, the sin of one of the angles is equal to the cosine of the complementary angle. Also, the tan of one angle is the reciprocal of the tan of the other complementary angle.
Review examples: Draw a diagram then answer the question.
1.) The area of a square is 100 square centimeters. What is the product of the lengths of the diagonals of the square?
2.) A parallelogram has sides that are 10 cm and 20 cm long. The measure of the acute angles of the parallelogram is 30 degrees. What is the area of the parallelogram?
3.) What is the area of a regular hexagon with sides that are 10 cm long?
4.) A road ascends a hill at an angle of 4 degrees. For every 100 feet of road, how many feet does the road ascend?
5.) According to the building codes, the maximum angle of ascent for a staircase in a home is 42.5 degrees. To get from the first floor to the second floor in a new home, a staircase will have a total vertical distance of 115.5 inches. What is the minimum horizontal distance, to the nearest inch, needed for the staircase?
EOCT Practice Items: Draw a diagram then answer the question.
1.) The length of one diagonal of a rhombus is 12 cm. The measure of the angle opposite that diagonal is 60 degrees. What is the perimeter of the rhombus?
a. 24 cm
b. 48 cm
c. cm
d.
2.) Angle J and angle K are complementary angles in a right triangle. The value of tan J is.
What is the value of sin J?
a.
b.
c.
d.
3.) Triangle RST is a right triangle with right angle S, as shown.
What is the area of triangle RST?
A. 6.15 square in
B. 6.54 square in
C. 46.47 square in
D. 49.45 square in
Unit 2: Right Triangle Test Review
Find the missing side lengths or angles measures. You may use
Pythagorean Theorem, Special Right Triangles or Trig Ratios
1. The legs of a right triangle measure 23 cm and 9 cm; what is the length of the hypotenuse?
2. The hypotenuse of a right triangle measures 33 m and one leg 20 m. What is the length of the
other leg?
3. 4. 5.
6. 7. 8.
9. 10. 11.
12. An equilateral triangle has a side with length 15. What is the length of the altitude of the
triangle? Draw a diagram to show how you solved this.
13. The length of a diagonal of a square is 24 inches. What is its perimeter? Draw a diagram.
A. 12 in. B. 24Ö2 in. C. 48Ö2 in. D. 48 in. E. 96 in.
14.
15. A new store is being built. An escalator is planned. It will make an angle of 37° with the floor. If the
vertical distance between floors is 15 feet, how long will the escalator be? Draw a diagram.
16. A sonar operator on a ship detects a submarine at a distance of 500 meters and an angle of
depression of 40°. How deep is the submarine?
17. In the diagram below, what is the measure of ÐB to the nearest tenth degree?
A. 42.8°
B. 47.2°
C. 33.7°
D. 1.5°
E. 56.3°
18. A pole in the ground measures 1.5 meters. It casts a shadow 2.4 meters long. What is the angle of elevation of the sun?
19. A ladder is to be placed against a building at a point 15 meters above the ground. The angle of elevation of the ladder must be no more than 40°. What should the length of the ladder be?
20. A person in a lighthouse spots a whale. The point form which the sighting is made is 23 meters above sea level. The angle of depression of the sighting is 12°. Find the distance between the lighthouse and the whale.