Math 5 Trigonometry Chapter 1 Test Name__________________________
Show all work for credit. Write all responses on separate paper.
1.
What angle has the same measure as its complement? How do you know?
2.
What is the complement of the supplement of 100˚ angle?
3. Given Quadrilateral ABCD with diagonal BD forming congruent angles and , what kind of quadrilateral do you think this is? Why? Give as persuasive a justification as you can.
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4.
Find
the perimeter of an isosceles triangle with base = 12cm and height = 4cm.
5.
Find the area of an isosceles triangle with sides of
length 2cm, 3cm and 3cm.
6.
Given that AC
= AB and AE = ED = DB = BC
in at right, find the degree measure of
7.
Carlos and Karla start at the north west corner of a
square block measuring 120 meters on a side and Carlos starts walking around
the block by heading east at 0.5 meters per second at the same time that Karla starts
walking around the block by heading south at 0.6 meters per second. What is the length of the line segment
connecting Carlos and Karla after five minutes?
8. Consider a 120˚ sector of a circle with radius 10cm.
a. Find the perimeter of the sector.
b.
Find the area of the sector.
9. In the diagram at right, AB is a diameter of the circle centered at O and C is a point on the perimeter of the circle.
a. Express in terms of .
b. Explain why is isosceles.
c. Express in terms of .
d.
Express
in terms of
.
10. In the figure at right,
a. Show that
b. Find the length of AE.
c. Draw BD. Is ? Why or why not?
Solutions
7. Since 5 minutes is 300 seconds, Carlos will travel (0.5 m/s)*300s = 150m, putting him at a point 30 m south of the north edge on the east side of the block. Karla will travel (0.6 m/s)*300s = 180m, so that she’s on the south edge, 60m east of the west side. Thus the distance between them is the hypotenuse of a right triangle with legs 60 and 90, D = m |
a. The perimeter of the sector is
b. The area of the sector is cm2
a. .
b. AD and DC are radii, so AD = DC.
c.
d.