Lesson 4 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

7.

The figure shows $2$ storage silos for grain. The diameter of each measures $24 feet$ and the height of the cylinder measures $51 feet$ . The height of the cone adds an additional $12 feet$ . Find the total volume of one silo.

8.

How many bushels of grain will each silo be able to store, if a bushel is $1.244 cubic feet$ ? (Assume it can be filled to the top.)

9.

Density relates to the degree of compactness of a substance. A cubic inch of gold weighs a great deal more than a cubic inch of wood because gold is more dense than wood. The density of grains also varies. Use the information given to calculate how many tons of each type of grain can be stored in one silo. ( $1 ton$ $= 2,000 lbs$ .)

$1 bushel$ of oats weighs $32 pounds$

$1 bushel$ of barley weighs $48 pounds$

$1 bushel$ of wheat weighs $60 pounds$

10.

A $\frac{3}{4}$ -ton pickup has the capacity to haul a little more than $1,500 lbs$ . If the hauling bed of the pickup measures $4 ft$ by $6.5 ft$ by $2 ft$ , can a $\frac{3}{4}$ -ton pickup safely haul a full (level) load of oats, barley, or wheat? Justify your answer for each type of grain.

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 $m ∠ D$ .