Lesson 6 You Nailed It! Practice Understanding

Ready

Use the given measures on the triangle to write the indicated trigonometric value. Write trigonometric ratios as a fraction. Then write them as a decimal rounded to thousandths place.

1.

$\sin A =$

$\cos A =$

$\tan A =$

2.

$\sin B =$

$\cos B =$

$\tan B =$

3.

$\sin P =$

$\cos P =$

$\tan P =$

4.

$\sin S =$

$\cos S =$

$\tan S =$

5.

Which trigonometric ratio is exact, the fraction or the decimal? Explain.

6.

My calculator tells me that $\frac{\sqrt{2}}{2} = 0.7071067812$ . Is one value more accurate than the other? Explain.

Set

Now that the deck is underway, Tatiana is ready for a new project. She has designed a fountain for the backyard. She has drawn a two-dimensional cross-section to model the fountain.

7.

Make a sketch of the fountain by rotating the cross-section about the $y$ -axis.

8.

Tatiana has added measurements to her design. In order to find the volume, she has divided the fountain into four parts. The base is a cylinder on which sits half of a sphere. Resting on the sphere is another, smaller cylinder topped by a small sphere. Find the volume of the fountain.

9.

Tatiana has built her fountain out of Styrofoam and spray painted it steel grey. The Styrofoam has a density of $3 \frac{lbs}{{ft}^{3}}$ . Find the weight of the Styrofoam fountain in $\frac{lbs}{{ft}^{3}}$ . (Write out the equation you use to find the weight, including the units.)

10.

A destructive wind storm has crushed Tatiana’s fountain. This time Tatiana plans to build the fountain out of high density polyethylene resin. It has a density of $60 \frac{lbs}{{ft}^{3}}$ . What will the finished fountain weigh?

Go

Quadrilateral $A B C D$ is a parallelogram.

11.

Given: $m ∠ B = 4 x - 5$ and $m ∠ D = 3 x + 10$

Find $m ∠ B$ and $m ∠ C$ .

12.

Given: $m ∠ B = 53 °$

Find $m ∠ A$ , $m ∠ C$ , and $m ∠ D$ .

13.

Given: $m ∠ A = 3 (m ∠ B)$

Find $m ∠ A$ and $m ∠ B$ .

14.

Given: $m ∠ A = 120 °$

Find $m ∠ B$ , $m ∠ C$ , and $m ∠ D$ .