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.

Triangle ABC with AB=26, AC=24, and BC=10. Angle C is a right angle.

2.

Triangle ABC with AB=41, BC=40, AC=9. Angle C is a right angle.

3.

Triangle PQR with PQ=21, PR=29, and QR=20. Angle Q is a right angle.

4.

Triangle RST with RS=39, RT=80, ST=89. Angle R is a right angle.

5.

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

6.

My calculator tells me that . 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 -axis.

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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.

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9.

Tatiana has built her fountain out of Styrofoam and spray painted it steel grey. The Styrofoam has a density of . Find the weight of the Styrofoam fountain in . (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 . What will the finished fountain weigh?

Go

Quadrilateral is a parallelogram.

Parallelogram ABCD with AD parallel to BC and AB parallel to DC.

11.

Given: and

Find and .

12.

Given:

Find , , and .

13.

Given:

Find and .

14.

Given:

Find , , and .