Similar Right Triangles
Pythagorean Theorem
Special Right Triangles
Trigonometric Ratios
Vectors
100
In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments. True or False?
True (Theorem 9.2)
100
Find the area of a right triangle with a side leg length of 7cm and hypotenuse of 10 cm. Round to nearest tenth.
A= 25 square cm
100
What are the two kinds of special right triangles?
Special right triangles are triangles with angle measures 45-45-90 or 30-60-90.
100
What does SOHCAHTOA stand for? What does it mean to solve a right triangle?
Sin= opp/hyp cos= adj/hyp tan=opp/ adj Solving a right triangle means to determine the measures of all six parts (the right angle, the two acute triangles, the hypotenuse, and the two legs)
100
Define magnitude of a vector AB
Magnitude is the distance from the initial point A to the terminal point B.
200
Complete and solve the proportion: x/12=?/8 where 12 is the altitude of a right triangle and the hypotenuse is 8+x. Round to the nearest tenth.
x/12=12/8 which leads to x=18. Now what do we call the value of 12?
200
State the Converse of the Pythagorean Theorem (Thm 9.5)
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
200
You are given a 30-60-90 triangle with a hypotenuse of 8. Find the other 2 side lengths (base and height of the triangle). Round to the nearest hundredth.
base: 4 height: 4 root 3 or 6.93
200
If right triangle MNP has lengths NP=15 and PM=7, find the length of MN, the angle M, and angle N. Round to the nearest tenth and nearest degree.
MN= 16.6 angle M= 65 degrees angle N=25 degrees
200
Two vectors are parallel if they have the same or opposite directions. True or false?
True.
300
In a right triangle, 12 is the hypotenuse of a right triangle, 6 is the base, and x is the smaller part of the hypotenuse when an altitude is drawn. Set up a proportion and solve for x. Round to the nearest tenth.
X=3
300
Is a triangle with side lengths 1, 2, and 3 a right triangle?
no
300
You are given a triangle whose hypotenuse is 4 inches and the other two legs are congruent. What kind of special right triangle is this and what is the length of the congruent legs? Round to the nearest hundredth.
45-45-90 ; 2.83
300
Part 1: Find the sin, cos, and tan of angles M and T of triangle MRT where MR=14, RT=10 and MT=the square root of 296. Round to the nearest hundredth Part 2: Also, if we have sin A= 0.24, solve for angle A.
Sin M= 0.5812, Cos M= 0.8137, Tan M= 0.7143 Sin T= 0.8137, Cos T= 0.5812, Tan T= 1.4 A= 13.9 degrees
300
Write the component form and magnitude of the vector PQ where P(0,0) and Q(3,4).
Component form <3,4> and magnitude is 5.
400
Write the Similarity statement for the three similar triangles formed in triangle PQR where QS is the altitude. Then find the length of QS if PS=8 and SR=10. Round to the nearest hundredth.
PQR~PSQ~QSR QS=8.94
400
Decide whether the numbers 5, 12, 13 represent the side lengths of a triangle. If they can, classify the triangle right, acute, or obtuse.
Yes, right triangle
400
The altitude of an equilateral triangle is 12 cm. Find the perimeter of the triangle. Round to nearest tenth.
Perimeter is 41.6 cm
400
Find the value of each variable in the right triangle where the base is 3, the height is X, and the hypotenuse is Y. The base angle is 72 degrees. Round to the nearest tenth.
x=9.2 and y=9.7
400
Let vector u=<2,-3> and v=<3,-2>. Find u+v
u+v=<5,-5>
500
In a right triangle WYZ where WY=5, WZ= 4, YZ=3, find the altitude XZ=? Round to the nearest tenth.
H=2.4 units
500
Find the area of a right triangle whose base is 5 inches and hypotenuse is 10 inches. Round to the nearest hundredth.
First find height, h= 8.66 inches Then find area, A=21.65 square inches
500
The perimeter of a rectangle is 66 cm. The length is twice the width. Find the length of the diagonal. Round to the nearest tenth.
The length of the diagonal is 24.6 cm.
500
A new store is being built. An escalator is planned. It will make an angel of 34 degrees with the floor. If the vertical distance between floors is 14 ft, how long will the escalator be? Draw a diagram. Round to the nearest tenth.
Sin 34= 14/x and x = 25 ft
500
If a point moves 7 spaces to the left and 4 down, what is the component form of the vector that describes this translation? Find the magnitude of the vector and round your answer to the nearest tenth.
<-7,-4> and magnitude is 8.1
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