Lesson 8 Relationships with Meaning Solidify Understanding

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1.

Write the formula for each measurement.

a.

Area of a circle

b.

Volume of a rectangular prism

c.

Volume of a cylinder

d.

Area of a rectangle

e.

Perimeter of a rectangle

f.

Circumference of a circle

2.

Find the perimeter and area for the rectangle.

3.

Find the circumference and area for the circle.

4.

Find the volume and surface area of the prism.

Set

Based on the given trigonometric ratio, sketch a triangle and find a possible value for the missing side as well as the other missing trigonometric ratios. Label angles $A$ and $B$ as the two non-right angles in the right triangle.

5.

$\tan (A) = \frac{3}{4}$ , $\tan (B) =$ .

$\sin (A) =$ , $\sin (B) =$ .

$\cos (A) =$ , $\cos (B) =$ .

Sketch of triangle:

6.

$\tan (A) =$ , $\tan (B) =$ .

$\sin (A) =$ , $\sin (B) = \frac{8}{17}$

$\cos (A) =$ , $\cos (B) =$ .

Sketch of triangle:

7.

$\tan (A) =$ , $\tan (B) =$ .

$\sin (A) =$ , $\sin (B) =$ .

$\cos (A) = \frac{12}{13}$ , $\cos (B) =$ .

Sketch of triangle:

8.

$\tan (A) =$ , $\tan (B) =$ .

$\sin (A) =$ , $\sin (B) = \frac{1}{\sqrt{2}}$

$\cos (A) =$ , $\cos (B) =$ .

Sketch of triangle:

Given a right triangle with angles $A$ and $B$ as the non-right angles. Determine if the statements are true or false. Justify your reasoning and show your argument.

9.

$\cos (A) = \frac{1}{\sin A}$

10.

$\tan (B) = \tan (90 - A)$

11.

$\tan (A) \cdot \cos (A) = \sin (A)$

Use a trigonometric equation to find the unknown side. Round values to the nearest tenth.

12.

13.

14.

Go

Find the slope of each line.

15.

16.

17.

Find the missing length in each right triangle. Then determine the slope of the hypotenuse given that the legs of the triangle are vertical and horizontal.

18.

Missing length:

Slope of hypotenuse:

19.

Missing length:

Slope of hypotenuse:

20.

Missing length:

Slope of hypotenuse: