Tangent Ratio (TOA)

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Show your work for each problem.

1.
What is the tangent ratio formula?
1. a)
2. b)
3. c)
4. d)
2.
What is the value of ?
1. a)
2. b)
3. c)
4. d)
3.
Which sides of a right triangle does tangent NOT use?
1. a)Hypotenuse
2. b)Opposite
3. c)Adjacent
4. d)All of the above
4.
What is ?
5.
In a right triangle with opposite side and adjacent side , what is ?
6.
What is ?
1. a)
2. b)
3. c)
4. d)
7.
If , what is the simplified value?
8.
If the opposite side is and the adjacent side is , what is ? Give your answer as a decimal.
9.
What happens to as approaches ?
1. a)It approaches 1
2. b)It stays constant
3. c)It approaches 0
4. d)It approaches infinity
10.
A tree casts a shadow meters long. If the angle of elevation from the tip of the shadow to the top of the tree is , find the height of the tree. (Use )
11.
A ramp rises feet over a horizontal distance of feet. Find the angle of the ramp. (Use )
12.
From a point meters from a building, the angle of elevation to the top is . Find the height of the building to the nearest meter. (Use )
13.
From the top of a cliff meters high, a boat is spotted at an angle of depression of . How far is the boat from the base of the cliff? (Use )
14.
A ladder reaches meters up a wall. The base of the ladder is meters from the wall. Find the angle the ladder makes with the ground. (Round to the nearest degree)
15.
A surveyor stands meters from a tower. The angle of elevation to the top is . The surveyor's eyes are meters above the ground. Find the total height of the tower. (Use )
16.
What is ? Express your answer in simplified radical form.