I love that joke

Updates
• Remember today is Wednesday, you’re supposed to be wearing pink
• Test make ups/corrections this afternoon
• Make up: exactly what you think
• Corrections: A shortened version of the test
• 2 multiple choice, solving sides, solving angles (5ea)
• 1 solving right triangle (10ea)
• 2 word problems (15 total)

Questions/Comments about
MathXL?

Question 1
The rocks at Stonehenge are arranged in a circular pattern (see figure). If the radius of the circle is 34.5 meters how far apart (direct line of sight) are the stones at 3 and 6 o’clock?

Question 1
The rocks at Stonehenge are arranged in a circular pattern (see figure). If the radius of the circle is 34.5 meters how far apart (direct line of sight) are the stones at 3 and 6 o’clock?
48.8 m

Question 2
A teleporter, living in Manhattan, starts out in her lair at the corner of 87 th St and 6 th Ave. Her first goal is to “jump” inside the bank on the corner of 5 th St and 9 th Ave, then make a swift get away to the top of the Empire State Building, on the corner of 34 th and 5 th . Assume one block is 0.25 km. Round answers to the nearest tenth of a kilometer.
a) How far was the jump from her lair to the bank?
b) How far was the jump from the bank to the Empire
State Building?
c) How far would the jump back to her lair from the
Empire State Building?

𝑎 2 + 𝑏 2 = 𝑐 2

𝑎 2 + 𝑏 2 = 𝑐 2
3 2 + 82 2 = 𝑐 2

𝑎 2 + 𝑏 2 = 𝑐 2
3 2 + 82 2 = 𝑐 2
9 + 6724 = 𝑐 2

𝑎 2 + 𝑏 2 = 𝑐 2
3 2 + 82 2 = 𝑐 2
6733 = 𝑐 2

𝑎 2 + 𝑏 2 = 𝑐 2
3 2 + 82 2 = 𝑐 2
6733 = 𝑐 2
6733 = 𝑐

𝑎 2 + 𝑏 2 = 𝑐 2
3 2 + 82 2 = 𝑐 2
6733 = 𝑐 2
6733 = 𝑐 𝑐 = 82.1

𝑎 2 + 𝑏 2 = 𝑐 2
3 2 + 82 2 = 𝑐 2
6733 = 𝑐 2
6733 = 𝑐 𝑐 = 82.1
82.1 blocks, so 20.5km

Question 2
A teleporter, living in Manhattan, starts out in her lair at the corner of 87 th St and 6 th Ave. Her first goal is to “jump” inside the bank on the corner of 5 th St and 9 th Ave, then make a swift get away to the top of the Empire State Building, on the corner of 34 th and 5 th . Assume one block is 0.25 km. Round answers to the nearest tenth of a kilometer.
a) 20.5 km b) How far was the jump from the bank to the Empire
State Building?
c) How far would the jump back to her lair from the
Empire State Building?

𝑎 2 + 𝑏 2 = 𝑐 2

𝑎 2 + 𝑏 2 = 𝑐 2
Filled in a & b

𝑎 2 + 𝑏 2 = 𝑐 2
Filled in a & b
Squared and added

𝑎 2 + 𝑏 2 = 𝑐 2
Filled in a & b
Squared and added
Square rooted
So….

𝑎 2 + 𝑏 2 = 𝑐 2
Filled in a & b
Squared and added
Square rooted
So….
Let’s square root the sum of the squares of the distances

𝑎 2 + 𝑏 2 = 𝑐 2
Filled in a & b
Squared and added
Square rooted
So….
Let’s square root the sum of the squares of the distances i.e., 𝒄 = 𝒂 𝟐 + 𝒃 𝟐

Question 2
A teleporter, living in Manhattan, starts out in her lair at the corner of 87 th St and 6 th Ave. Her first goal is to “jump” inside the bank on the corner of 5 th St and 9 th Ave, then make a swift get away to the top of the Empire State Building, on the corner of 34 th and 5 th . Assume one block is 0.25 km. Round answers to the nearest tenth of a kilometer.
a) 20.5 km b) 7.3 km c) How far would the jump back to her lair from the
Empire State Building?

Question 2
A teleporter, living in Manhattan, starts out in her lair at the corner of 87 th St and 6 th Ave. Her first goal is to “jump” inside the bank on the corner of 5 th St and 9 th Ave, then make a swift get away to the top of the Empire State Building, on the corner of 34 th and 5 th . Assume one block is 0.25 km. Round answers to the nearest tenth of a kilometer.
a) 20.5 km b) 7.3 km c) 13.3 km

The Distance Formula
In general
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐷𝑖𝑠𝑡 2 + 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐷𝑖𝑠𝑡 2
In the coordinate plane (XY plane):
Given the points 𝑃 = 𝑥
1
, 𝑦
2 and 𝑄 = 𝑥 the Euclidean distance between them is 𝐷
2
, 𝑦
2
𝐷 = 𝑥
1
− 𝑥
2
2 + 𝑦
1
− 𝑦
2
2

Question 3
Agree or Disagree (circle your option)
It is likely that one day Sean Combs (aka Puffy
Daddy) will be the mayor of New York City. Why else do you think we never hear from him anymore?

Question 4
Find the distance between the two points (3, 5) and
(-4, 8). Round answer to the nearest tenth.

Question 4
Find the distance between the two points (3, 5) and
(-4, 2). Round answer to the nearest tenth.

Question 5
Find the mid-point between the two points (3, 5) and
(-4, 2). Round answer to the nearest tenth.

Question 5
Find the mid-point between the two points (3, 5) and
(-4, 2). Round answer to the nearest tenth.

Question 5
Find the mid-point between the two points (3, 5) and (-4, 2). Round answer to the nearest tenth.

Question 5
Find the mid-point between the two points (3, 5) and (-4, 2). Round answer to the nearest tenth.

Question 5
Find the mid-point between the two points (3, 5) and (-4, 2). Round answer to the nearest tenth.

Question 5
Find the mid-point between the two points (3, 5) and (-4, 2). Round answer to the nearest tenth.
• We draw in two right triangles with equivalent hypotenuses

Question 5
Find the mid-point between the two points (3, 5) and (-4, 2). Round answer to the nearest tenth.
• We draw in two right triangles with equivalent hypotenuses
• The yellow and purple triangles are congruent via AAS (the right angle, the green angle, and the hypotenuse)

Question 5
Find the mid-point between the two points (3, 5) and (-4, 2). Round answer to the nearest tenth.
• We draw in two right triangles with equivalent hypotenuses
• The yellow and purple triangles are congruent via AAS (the right angle, the green angle, and the hypotenuse)
• Therefore the horizontal and vertical legs of the purple and yellow triangle are the same

Question 5
Find the mid-point between the two points (3, 5) and (-4, 2). Round answer to the nearest tenth.
• We draw in two right triangles with equivalent hypotenuses
• The yellow and purple triangles are congruent via AAS (the right angle, the green angle, and the hypotenuse)
• Therefore the horizontal and vertical legs of the purple and yellow triangle are the same
• Hence the mid point is the average of both coordinates

Question 5
Find the mid-point between the two points (3, 5) and
(-4, 2). Round answer to the nearest tenth.
−4 + 3
,
2
2 + 5
2

Question 5
Find the mid-point between the two points (3, 5) and
(-4, 2). Round answer to the nearest tenth.

The Mid-Point Formula
Given the two points 𝐴 = 𝑥
1
, 𝑦
1 and 𝐵 = 𝑥
2 mid-point between them is found at 𝐶 such that
, 𝑦
2 the
𝐶 = 𝑥
1
+ 𝑥
2
, 𝑦
1
2
+ 𝑦
2
2

The Mid-Point Formula
Given the two points 𝐴 = 𝑥
1
, 𝑦
1 and 𝐵 = 𝑥
2 mid-point between them is found at 𝐶 such that
, 𝑦
2 the
𝐶 = 𝑥
1
+ 𝑥
2
, 𝑦
1
2
+ 𝑦
2
2 i.e., the average of the coordinates

Trig. Word Problems

Review Ex 1 – Trig Word Probs.
A captain of a boat stands on deck with a digital hypsometer looking at a land beacon.
The hypsometer gives an angle of elevation reading of 18.5
0 and a direct distance reading of 0.44 miles. How far from the beacon is the boat?

Review Ex 2 – Trig Word Probs.
Jim stands in a tree looking at Susie with an angle of depression measuring 70 0 . The point in the tree where Jim is standing is 12 feet off the ground. How far would Jim have to throw a pebble if he wanted to hit Susie?
Assume the pebble travels in a straight line path.

Review Ex 3 – Trig Word Probs.
Sampson aims his sling shot at Goliath’s head with an angle of elevation measuring
62 0 and hits him square between the eyes.
How far from Goliath’s feet is Sampson standing if Goliath is 23 feet tall? Round to the nearest tenth of a foot.

Review Ex 3 – Trig Word Probs.
Sampson aims his sling shot at Goliath’s head with an angle of elevation measuring
62 0 and hits him square between the eyes.
How far from Goliath’s feet is Sampson standing if Goliath is 23 feet tall? Round to the nearest tenth of a foot.
12.2 feet away

Review Ex 4 – Trig Word Probs.
A ship’s navigator observes the measure of the angle of elevation to the top of a cliff, that the boat is headed directly towards, to be 64 0 . An hour later, traveling straight at the cliff, he noticed the angle of elevation has changed to 79 0 . How far has the shipped moved if the cliff is 75 meters tall?

Review Ex 4 – Trig Word Probs.

Review Ex 4 – Trig Word Probs.
The boat traveled 22 meters in that hour