Finding Missing Angles

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Show your work for each problem.

1.
If $\sin(\theta) = 0.5$ , what is $\theta$ ?
1. a) $90°$
2. b) $30°$
3. c) $60°$
4. d) $45°$
2.
Which inverse function should you use if you know the opposite and adjacent sides?
1. a) $\cos^{-1}$
2. b) $\tan^{-1}$
3. c) $\sin^{-1}$
4. d)Pythagorean Theorem
3.
Calculate: $\tan^{-1}(1)$ = ?° (Give your answer in degrees)
4.
If $\cos(\theta) = 0.5$ , what is $\theta$ ? (Answer in degrees)
5.
In a right triangle, the opposite side is 4 and the hypotenuse is 5. What is the angle? (Round to the nearest degree)
1. a) $45°$
2. b) $37°$
3. c) $53°$
4. d) $39°$
6.
A ramp rises 3 meters over a horizontal distance of 8 meters. Find the angle of inclination.
7.
A ladder 10 meters long leans against a wall. The foot of the ladder is 6 meters from the wall. Find the angle between the ladder and the ground.
8.
A building 21 meters tall casts a shadow 25 meters long on level ground. What is the angle of elevation of the sun? (Round to the nearest degree)
9.
What is $\sin^{-1}(\sin(150°))$ ?
1. a) $-30°$
2. b) $30°$
3. c) $210°$
4. d) $150°$
10.
A plane is at altitude 8000 feet and must descend to land, starting 30000 feet horizontally from the runway. Find the descent angle to the nearest tenth of a degree.
11.
In a right triangle, one leg is 7 and the other is 24. Find both acute angles (to the nearest tenth of a degree).
12.
A surveyor stands 150 meters from the foot of a cliff that is 121.5 meters high. Her measuring instrument is 1.5 meters above the ground. What is the angle of elevation from the instrument to the top of the cliff? (Round to the nearest tenth of a degree)
13.
A guy wire is attached to a pole 12 meters up from the ground and anchored 5 meters from the base. Find the angle the wire makes with the ground.
14.
Why does $\sin^{-1}(1.5)$ give an error on your calculator?
1. a)Sine values only range from $-1$ to $1$
2. b)The angle is too large
3. c)You need to use arcsin instead
4. d)The calculator is in radian mode
15.
A roof has a pitch of 8/12 (rises 8 feet for every 12 feet horizontal). What is the roof angle to the nearest degree?