Definitions
How do you find the hypotenuse of a triangle?
Side opposite from the right angle
Longest side of the a right triangle
Explain how to find the length of a side of a right triangle if you know the length of a side and the hypotenuse.
Square the hypotenuse and side, subtract the side from hypotenuse, then square root.
In a right triangle, if the adjacent side is 17 units and the angle is 59 degrees, what is the length of the hypotenuse?
33.0 units
cos (59) = 17 / x
A ladder is leaning against a wall forming a right triangle with the ground. If the ladder is 10 feet long and the foot of the ladder is 6 feet from the wall, how high does the ladder reach on the wall?
8 feet
102-62=a2
What is today's date?
March 13, 2025
What is the Pythagorean Theorem?
a2+b2=c2
If one leg of a right triangle is 3 units and the other leg if 4 units, what is the length of the hypotenuse?
5 units
32+42=c2
If a right triangle has an angle of 24 degrees and the adjacent side is 5 units long, what is the length of the opposite side?
2.2 units
tan(24) = x / 5
An airplane is flying at an altitude of 5,000 feet. If it is 3,000 feet horizontally from the point directly below it, what is the angle of depression from the airplane to the ground?
59 degrees
2nd, tan-1 (5,000/3,000)
What is our school mascot?
Rebel
What is the sine ratio in a right triangle?
opposite / hypotenuse
Prove that the triangle with sides 5, 12, and 13 is a right triangle.
Check that 52+122=132.
25+144=169
169=169
In a right triangle, if the adjacent side is 40 units and the hypotenuse is 51 units, what is the measure of the angle?
38.3 degrees
2nd, cos-1 (40/51)
A tree casts a shadow that is 10 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 30 degrees, how tall is the tree?
6 feet
tan(30) = x / 10
What have we been learning this week?
Trigonometric Ratios
How would you find the cosine of an angle in a right triangle?
adjacent / hypotenuse
A triangular park has sides measuring 8 meters, 15 meters, and 17 meters. Is it a right triangle?
Yes, it is a right triangle.
82+152=172
64+225=289
289=289
If a right triangle has an angle of 30 degrees and the hypotenuse measures 10 units, what is the length of the opposite side?
5 units
sin(30)=x/10
You are standing 50 meters from the base of a tower. If the angle of elevation to the top of the tower is 60 degrees, how tall is the tower?
86.6 meters
tan(60)= x / 50
When is Spring Break?
April 24-28
Week after next!
What is the tangent ratio?
opposite / adjacent
If a right triangle has a hypotenuse of 10 units and one leg of 6 units, what is the length of the other leg?
8 units
102-62=a2
In a right triangle, if the opposite side is 8 units and the adjacent side is 6 units, what is the measure of the angle?
53 degrees
2nd, tan-1 (8/6)
Calculate the angle that would form with the ground if a ladder of length 15 feet leans against a wall, reaching a height of 12 feet.
53.1 degrees
sin (x) = 12 / 15
When will we have our test?
Tuesday!!
March 18th!!