Angles and measurement
What is the formula for pythagorean theorem?
a^2+b^2=c^2
In a right-angled triangle, if the opposite side to angle AAA is 4 units and the hypotenuse is 5 units, what is sinA\sin AsinA?
sinA=Opposite/hypotenuse=4/5=0.8
Two triangles have sides of 5 cm and 7 cm with an included angle of 60°. Are they congruent?
Yes; by SAS (Side-Angle-Side).
when the angles are the same just in a different location ?
corresponding angles
What is the probability of rolling a 3 on a standard six-sided die?
There is one favorable outcome (rolling a 3) out of six possible outcomes. Because there are six sides on a dice, meaning its a one and six chance
Triangles with sides 6 cm, 8 cm, and 10 cm. Are they congruent?
Yes; by SSS (Side-Side-Side)
what is the name of two angles that measure to 180?
supplementary angles
In a right-angled triangle, the adjacent side to angle BBB is 3 units, and the hypotenuse is 7 units. What is cosB\cos BcosB, and what is the measure of angle BBB in degrees?
CosB=adjacent/hypotenuse=3/7=0.4286\
How to get B=
cos^-1(0.4826)= 64.3=B
Two triangles have angles of 50° and 60°, and the side between them is 7 cm. Are they congruent?
Yes; by ASA (Angle-Side-Angle).
In triangle EFG angle e measures 90, angle F is 27, what is the measurement of angle G?
63
A bag contains 2 red and 3 blue marbles. If one marble is drawn at random, what is the probability that it is red?
if there are 5 total marbles(2 red and three blue) the chance of getting a blue marble is 3/5, as getting a red is 2/5
Right triangles with hypotenuse 13 cm and one leg 5 cm. Are they congruent?
Yes; by RHS (Right angle-Hypotenuse-Side).
what is the distance between these two points :
point 1:(3,5)
point 2:(4,6)
1.41 units.: here is how i found it
d=(x2-x1)^2+(y2-y1)^2
In triangle ABCABCABC, side AB=7AB = 7AB=7 units, side AC=9AC = 9AC=9 units, and angle A=60∘A = 60^\circA=60∘. Find the length of side BCBCBC.
BC2=AB2+AC2−2⋅AB⋅AC⋅cos(A)
BC2=72+92−2⋅7⋅9⋅cos(60∘)
BC2=49+81−126⋅0.5=130−63=67
BC=67=8.19 units
Triangles have angles of 70° and 60°, and a non-included side of 9 cm. Are they congruent?
Yes; by AAS (Angle-Angle-Side).