The legs of a 45-45-90 triangle are congruent. What is another name for this triangle?
Isosceles Right Triangle
100
If the altitude is drawn to the hypotenuse of a right triangle, then......
the two triangles formed are similar to the original triangle and to each other.
100
Find the geometric mean between 16 and 24. Write your answer in simplest form.
8√6
100
Using diagram A, find x to the nearest integer. (equation and answer)
cos 42 = x/100
x = 74
100
From a point on the ground 100 meters from the foot of a cliff, the angle of elevation of the top of the cliff is 24 degrees. How high is the cliff? (equation and answer)
tan 24 = x/100
Therefore, the cliff is about 45 meters high.
200
What does the following symbol mean: ≈ ?
Approximately equal to
200
State the complete Pythagorean Theorem.
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
200
Using diagram F, find the values of x, y, and z.
x = 5.4
y = 9.6
z = 7.2
200
Using diagram B, find the measure of x to the nearest integer. (equation and answer)
tan 38 = 88/x OR tan 52 = x/88
x = 113
200
A road climbs at an 8 degree angle with the horizontal. What is the grade of the road? (provide equation and give the answer as a percent)
tan = x/100
Therefore, the grade of the road is about 14%.
300
Tangent is the ratio of the lengths of the _________ of a right triangle.
Legs
300
State the converse of the Pythagorean Theorem.
If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
300
Refer to diagram G to find c, given that a = 6 and b = 9. Write your answer in simplest form.
3√13
300
Using diagram C, find the measure of angle D to the nearest degree. (equation and answer)
sin D = 24/25 or cos D = 7/25 or tan D = 24/7
measure of angle D = 74 degrees
300
Two buildings on opposite sides of a street are 40 meters apart. From the top of the taller building, which is 185 meters high, the angle of depression to the top of the shorter building is 13 degrees. Find the height of the shorter building.
tan 13 = x/40
Therefore, the height of the shorter building is about 176 meters.
400
In a right triangle, cosine is the ratio of what? (No abbreviations or acronyms!)
Length of the leg adjacent to the angle: length of the hypotenuse
400
If the square of the longest side of a triangle is less than the sum of the squares of the other two sides then...
the triangle is acute.
400
Refer to diagram H to find the value of y to the nearest degree.
y = 23 degrees.
400
Using diagram D, find r and p to the nearest integer. (equation and answer)
sin 30 = r/150
tan 40 = 75/p
r = 75, p = 89
400
Joe, on the ground, looks up at Sara in a hot air balloon at a 35 degree angle of elevation. If Joe and Sara are 500 feet apart, about how far off the ground is Sara? (equation and answer)
sin 35 = y/500
Therefore, Sara is about 287 feet off the ground.
500
Given a, b, and x are positive numbers and a:x = x:b, what is x in relation to a and b?
x is the geometric mean between a and b.
500
In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg and....
the longer leg is √3 times as long as the shorter leg.
500
Find the measures of the three angles, to the nearest degree, in the triangle with the lengths of sides: 18, 24, 30.
The triangle is a right triangle.
Therefore, the angle measures are 90, 53 and 37 degrees.
500
Using diagram E, find y to the nearest integer.
y = 108
500
A rhombus, has diagonals of length 4 and 10. Find the angles of the rhombus to the nearest degree.