Geometry Midterm Spring'25

Sin/Cos/Tan

100

If the sinϴ = 2/3. What is the csc

3/2

200

If the cos(ϴ)=4/5, what is the tan(ϴ)

3/4

300

What is the tan of a 45 degree angle in a 45-45-90 triangle?

1

400

What is the cos(x), if the sin(x) = 2 / 5 ?

√(21)/5

500

What is the tan(x), if the cos(x) = 7 / 15? Round to the nearest hundreth.

1.90

Special Triangles

100

The opposite side of a 45* angle is 3. What are the lengths of the other two sides?

Adjacent: 3

Hypotenuse: 3√ 2

200

The opposite side of a 60* angle is 5√ 3. What are the lengths of the other two sides?

Adjacent: 5

Hypotenuse: 10

300

The hypotenuse of a 45-45-90 triangle is 13 cm long. What is the length of the other two sides?

Both sides are each 13/√ 2cm

400

What is the cos of the 60* angle of a 30-60-90 triangle?

√(3)/2

500

The hypotenuse of a 30-60-90 triangle is 50 m. What are the length other two sides?

Short side: 25 m

Long side: 25√ 3 m

Circles

100

What is 211º in radians?

3.68

200

What is 1.87 radians in degrees?

107.14*

300

If a circle has a diameter of 10cm. What is length of the circumference in cm?

10π cm

or

31.42 cm

400

A circle has an arc of 3.03, and a radius of 6. What is the measure of the angle that intercepts the arc?

28.93

500

Complete the square of this circle to discover it's center and radius: 

x² + y² - 10x - 16y + 17 = 0

x²- 10x + 25 + y² - 16y + 64 = -17 +25 + 64

(x-5)² + (y-4)² = 72

Midpoint (5,4)

Radius √ 72

Parabolas, Hyperbolas, and Ellipses

100

Write the equation for a parabola that has a focus of (-3, 1), and a directrix of 0.

(1/2)x² + 3x + 5 = y

200

Write an equation for an ellipse with the foci at (0, 6) and (0, -6), and vertices at (4, 0) and (-4, 0)

x² / 16 + y² / 52 = 1

300

Use the focus and directrix to find the equation of a parabola that has a focus of (4, 7), and a directrix of 3.

(1/8)x² - x + 7 = y

400

Write an equation for a hyperbola that has foci at (5, 0) and (-5, 0), and vertices at (4, 0) and (-4, 0)

x² / 16 - y² / 9 = 1

500

Write the equation for a hyperbola that has the foci at (0, 11) and (0, -11) and the vertices at (0,6) and (0,-6)

y² / 36 - x² / 85 = 1

MIXED

100

What is the law of Sines?

a/Sin(A)=b/Sin(B)= c/Sin(C)

200

What is the law of Cosines?

a² = b² + c² – 2bcCos(A)

300

(x-h)²/a² - (y-k)²/b² =1 

is the formula for what function?

Hyperbola

400

What special triangle has side lengths that measure 1,2, √ 3 ?

30-60-90 triangle

500

Write an equation for an ellipse that has foci at (0, 10) and (0, -10), and vertices at (8, 0) and (-8, 0).

x² / 64 + y² / 164 = 1