Similar Triangles & Trigonometry
What is the sum of the angles in any triangle?
180°
What is the general form of a linear equation?
y=mx+b
What is the slope formula for a line?
M= Y2-Y1/X2-X1
What is a linear system?
A linear system is two or more linear equations that are solved at the same time to find a common solution (the point where the lines intersect).
What is the general form of a quadratic equation?
y=ax2+bx+c
Two triangles have angles of 40°, 60°, and 80°. Are they similar?
Yes — triangles are similar if their corresponding angles are equal.
Solve for x:
2x+3=11
2x=11−3⇒2x=8⇒x=4
What is the slope of a line passing through the points (3, 7) and (5, 11)?
m= 11-7/5-3 = 4/2 =2
How many possible solutions can a linear system have?
One solution (lines intersect at one point)
No solution (lines are parallel)
Infinite solutions (lines are the same)
What shape does the graph of a quadratic relation make?
A parabola (U-shaped curve).
In similar triangles, if one side in Triangle A is 5 cm and the matching side in Triangle B is 10 cm, what is the scale factor from A to B?
Scale factor=10/5+2
Solve for x:
5x−2=3x+6
5x−3x=6+2⇒2x=8⇒x=4
A line has a slope of 4 and passes through the point (2, 3). What is the equation of the line in the form y=mx+by = mx + by=mx+b?
y=4x−5
Solve the system by substitution
y=2x+1
y=5x−5
(2,5)
In the quadratic equation y=2x2−4x+1y what is the value of a, b, and c?
a=2, b=−4, c=1
A building casts a shadow 18m long. At the same time, a 2m stick casts a shadow 3m long. How tall is the building?
use similar triangles
2/3=h/18
Cross multiply
3h=36 ⇒ h=12m
Solve for x
2x+1/2 =7
x=13/3
etermine if the points (1, 4), (3, 10), and (5, 16) lie on the same line
10-4/3-1= 6/2 =3
Solve the system by elimination:
3x+2y=16
5x−2y=4
(2.5,4.25)
What is the vertex of the quadratic relation
y=(x−3)2+5
(3,5)
A tree casts a 12m shadow. The angle of elevation to the top of the tree is 35°. How tall is the tree? (Round to one decimal place)
tan(θ)= opp/Adj
tan(35°)= h/12
h=12×tan(35°)≈12×0.7002=8.4m
A babysitter charges a $20 flat fee plus $12 per hour. Write the equation to represent the total cost (C) for h hours.
C=12h+20
A line has a slope of -3 and passes through the point (-2, 5). Write the equation of the line.
y=−3x−1
A movie theatre sold 20 tickets for a total of $210. Adult tickets cost $15 each and child tickets cost $10 each. How many of each were sold? (Use a system)
y=20−2=18
The path of a soccer ball is modeled by the equation
y=−x2+6x+2
11 Units