Download GSE GeometryUnit 3 Right Triangle TRIGSTUDY GUIDE FOR CDA

GSE Geometry
Unit 3 Right Triangle TRIG
STUDY GUIDE FOR CDA
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1. A right triangle (shown below) has a hypotenuse with a length of 18 inches and a leg with
a length of 7 inches. Find the measure of angle B (round to the tenths place).
Hint: Use inverse buttton to find the angle
18
7
2. Luis is standing on a street in New York City looking at the top of the Empire State
Building with a 30° angle of elevation. He is 728.9 meters from the Empire State
Building.
728.9 m
How tall is the Empire State Building?
Hint: Determine which trig function is given sin, cos, tan, then solve for the missing side)
3. The legs of the isosceles triangle each measure 21 inches. Find the length of the
hypotenuse. (*Hint: Pythagoreans Theorem)
21 in.
21 in.
GSE Geometry
Unit 3 Right Triangle TRIG
STUDY GUIDE FOR CDA
4. Eric is flying an airplane at an altitude of 3400 feet. He sees his house on the ground at a
45o angle of depression.
3400 ft
What is Eric’s horizontal distance from his house at this point?
Hint: Alt. Int. Angles copy the 450 inside the triangle, set up trig ratio and solve for missing
side.
5. In the following triangle, 𝑏 = 11√3, what is the value of a?
6. The following drawing shows the plan for the big hill on a new roller coaster at an
amusement park.
163 feet
163 feet
What is the approximate length of the big hill track? Hint: Pythagoreans Thm
GSE Geometry
Unit 3 Right Triangle TRIG
STUDY GUIDE FOR CDA
A right triangle (shown below) has a hypotenuse with a length of 5 inches and a leg with a length
of 4 inches. Hint: Find missing side then set up each trig ratio
5
4
7. What is the sin A?
8. What is the cos A?
9. What is the tan A?
10. In the following diagram, a 27-foot slide is attached to a swing set. The slide makes a 65°
angle with the swing set.
27 ft
What is the height of the top of the slide?
Hint: Determine Trig Ratio to use and solve for missing side
GSE Geometry
Unit 3 Right Triangle TRIG
STUDY GUIDE FOR CDA
11. A broadcast antenna is situated on top of a tower. The signal travels from the antenna to
your house so you can watch TV. The angle of elevation from your house to the tower measures
30° and the distance from your house to the tower is 457 feet. Find the height of the tower.
(Round to the nearest tenth) Hint: Determine which trig ratio to use based on angle
457 ft
12. The diagonal of the square is 9√2 centimeters. Find the length of the sides of the square.
Hint: Same as # 13 use Pythagoreans Theorem; the lengths of the sides are equal because it a
square
9√2 𝑐𝑚
13. In the following triangle, what is the value of x? Hint: Pythagoreans Theorem
17 cm
GSE Geometry
Unit 3 Right Triangle TRIG
14. In the following figure, if tan 𝑥 =
STUDY GUIDE FOR CDA
12
5
, what are sin x and cos x?
Hint: Plug in the numbers in the picture and use them to set up the fraction for the sin x and the cos x; you
will need to find one missing side using Pythagoreans Theorem
15. What is the measure of Angle P (round to the nearest degree) AND the length of PN (round to
the nearest cm)?
Hint: Determine which trig function is given and set up a ratio to find the angle and another one
to find the length of PN)
35 cm
12 cm
16. In the following diagram, m B = 33and AB = 27 feet. What equation can be used to
find the value of x?
Hint: Determine which trig function is given and set up the ratio
27 ft
33
GSE Geometry
Unit 3 Right Triangle TRIG
STUDY GUIDE FOR CDA
5
17. Angles A and B are complementary angles in a right triangle. The value of tan B is 12 . What is the
value of cos A? Hint: When in doubt, DRAW IT out! Plug in the numbers in the picture; then set up new
ratios
20
18. Angles X and Y are complementary angles in a right triangle. The value of sin X = 29. Find
the cos and tan of X and the sin, cos, and tan of Y. Hint: Plug numbers in picture, solve for
missing side, then set up the trig ratios (fractions) That’s 5 different answers!
19. If the value of sin 25o = 0.42, then the cos _____ = 0.42?
Hint: Remember the sin and cos go with the complementary angles rule = 90
20. Using the triangle below, what measures are equivalent? Hint: recall the complementary
angles = 90