Finding Missing Sides

Show your work for each problem.

1.
In a right triangle with angle , if you know the hypotenuse and want to find the opposite side, which formula should you use?
1. a)
2. b)
3. c)
4. d)
Answer:
Since , we multiply both sides by hypotenuse to get: .
2.
A ladder meters long leans against a wall at a angle with the ground. Which calculation gives the height the ladder reaches?
1. a)
2. b)
3. c)
4. d)
Answer:
The height is opposite to the angle, and we know the hypotenuse (ladder = m). Using SOH: m.
3.
Calculate: . (Round to one decimal place)
Answer: 4
4.
Calculate: . (Round to one decimal place)
Answer: 6
5.
From a point m from the base of a tower, the angle of elevation to the top is . Which calculation finds the tower's height?
1. a)
2. b)
3. c)
4. d)
Answer:
We know the adjacent ( m) and want the opposite (height). TOA: , so height m.
6.
A ramp makes a angle with the ground and rises meters. How long is the ramp? (Round to one decimal place)
Answer: 7.2
, so m.
7.
A cable meters long supports a pole at an angle of with the ground. How high up the pole does the cable attach?
Answer: 19.2
1. What is the cable in this problem (opposite, adjacent, or hypotenuse)? hypotenuse
2. What are we trying to find (opposite, adjacent, or hypotenuse)? opposite
3. Which ratio uses opposite and hypotenuse? sine
4. Calculate . (Round to one decimal) 19.2
8.
A plane descends at a angle. After traveling meters along the flight path, how much altitude has it lost?
Answer: 139.5
1. What does the m represent (opposite, adjacent, or hypotenuse)? hypotenuse
2. What are we finding (opposite, adjacent, or hypotenuse)? opposite
3. Which trig ratio should we use? sine
4. Calculate . (Round to one decimal) 139.5
9.
Which formula would you use to find the adjacent side if you know the hypotenuse and angle ?
1. a)
2. b)
3. c)
4. d)
Answer:
Since , multiply both sides by hypotenuse: .
10.
A guy-wire is anchored meters from the base of a vertical antenna. If the wire makes a angle with the ground, how long is the wire? (Round to one decimal)
Answer: 48.5
, so m.
11.
A ship sails km on a bearing of east of north. How far east has the ship traveled?
Answer: 10.3
1. What is the km in this triangle? hypotenuse
2. The eastward distance is which side relative to the angle? opposite
3. Which trig function relates opposite and hypotenuse? sine
4. Calculate . (Round to one decimal) 10.3
12.
A ski slope is meters long with an angle of . What is the vertical drop of the slope?
Answer: 211.3
1. What does the m represent? hypotenuse
2. What are we finding - the vertical drop is which side? opposite
3. Which ratio should we use? sine
4. Calculate . (Round to one decimal) 211.3
13.
A surveyor stands m from the base of a cliff. The angle of elevation to the top is . How tall is the cliff? (Round to one decimal)
Answer: 111.9
, so m.
14.
A zip line is anchored meters high on a tower and makes a angle with the ground. How long is the zip line cable?
Answer: 226.9
1. The m height is which side relative to the angle? opposite
2. What are we trying to find? hypotenuse
3. Which formula do we need? (Write as: side = formula) hypotenuse = opposite / sin(theta)
4. Calculate . (Round to one decimal) 226.9
15.
A student calculated to find the hypotenuse. What information did they start with?
1. a)Opposite = m, angle =
2. b)Adjacent = m, angle =
3. c)Hypotenuse = m, angle =
4. d)Adjacent = m, angle =
Answer: Adjacent = m, angle =
From , rearranging gives . So they knew the adjacent side ( m) and the angle ().