If and are each first quadrant angles, which of the following must be true if sin = cos ?
a. + = rad b. + = 90
c. = /2 rad d. =
[Ques. 2] Consider the cosine of any angle between 35 and 40. If the angle were doubled, what would happen to the cosine of the angle.
a. It would halve.
b. It would decrease to less than half its original value.
c. It would decrease but be more than half its original value.
d. In different cases, it could do any of the above.
[Ques. 3] Consider the sine of any angle between 30 and 40. If the angle were doubled, what would happen to the sine of the angle?
a. It would double.
b. It would more than double.
c. It would increase but be less than double.
d. In different cases, it could do any of the above.
[Ques. 4] A train slowly climbs a 400-m mountain track which is at an angle of 8.0 with respect to the horizontal. How much altitude does it gain?
a. 55.7 m
b. 200 m
c. 60.7 m
d. 396 m
e. 400 m
[Ques. 5] A triangle has sides of length 7 cm and 11 cm. If the triangle is a right triangle, which of the following could be the length of the third side, to the nearest centimeter?
a. 11 cm
b. 8 cm
c. 16 cm
d. 17 cm
e. 7 cm
[Ques. 6] If = 90 , what is the value of sin2 + sin2 ?
a. 0
b. 1
c. 1
d. The answer depends on .
[Ques. 7] A right triangle has sides 10 m, 5 m, and 11 m. The smallest angle of this triangle is nearest
a. 32.
b. 27.
c. 22.
d. 63.
e. Not attainable since this is not a right triangle.
[Ques. 8] Suppose the interior angles of a triangle are 1, 2, and 3, with 1 > 2 > 3 . Which side of the triangle is the shortest?
a. The side opposite 1 b. The side opposite 2.
c. The side opposite 3 d. More information is needed unless the triangle is a right triangle.
[Ques. 9] A surveyor stands 100 m from the base of a building, and uses a transit to determine that the angle of elevation to the building's roof is 19.0. If the transit height is 0.80 m, what is the height of the building?
a. 94.6 m
b. 95.4 m
c. 35.2 m
d. 34.4 m
[Ques. 10] Each edge of a cube has a length of 12.7 cm. What is the length of a diagonal of the cube going through the center of the cube?
a. 24.0 in.
b. 22.0 in.
c. 25.5 in.
d. 20.5 in.
e. 8.7 in.
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