Mary Jane Sterling - Pre-Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

403. A submarine traveling 8 mph is descending at an angle of depression of 5°. How many minutes does the submarine take to reach a depth of 90 feet?

404. You’re a block away from a building that is 820 feet tall. Your friend is between you and the building. The angle of elevation from your position to the top of the building is 42°. The angle of elevation from your friend’s position to the top of the building is 71°. To the nearest foot, how far are you from your friend?

405. A lighthouse is located at the top of a hill 100 feet tall. From a point P on the ground, the angle of elevation to the top of the hill is 25°. From the same point P , the angle of elevation to the top of the lighthouse is 50°. How tall is the lighthouse?

406. A surveyor needs to find the distance BC across a lake as part of a project to build a bridge. The distance from point A to point B is 250 feet. The measurement of angle A is 40°, and the measurement of angle B is 112°. What is the distance BC across the lake to the nearest foot?

Illustration by Thomson Digital

407−410Find the length of the side indicated by x.

407.

Illustration by Thomson Digital

408.

Illustration by Thomson Digital

409.

Illustration by Thomson Digital

410.

Illustration by Thomson Digital

411−415Convert the radian measure to degrees. Round any decimals to two places.

411.

412.

413.

414. 3

415. 0.93

416−420Convert the degree measure to radians. Give the exact measure in terms of .

416. 225°

417. 60°

418. −405°

419. 36°

420. 167°

421−422The terminal side of an angle in standard position on the unit circle contains the given point. Give the degree measure of .

421.

422.

423−425The terminal side of an angle in standard position on the unit circle contains the given point. Give the radian measure of .

423.

424.

425.

426−430Find the reference angle for the angle measure. (Recall that the quadrants in standard position are numbered counterclockwise, starting in the upper right-hand corner.)

426. 167°

427. 342°

428. 265°

429. 792°

430. −748°

431−434Find the exact value of the trigonometric function. If any are not defined, write undefined .

431. sin 225°

432. tan 330°

433. cos 405°

434.

435−440Use the given information to find the exact value of the trigonometric function.

435. Given: ; is in quadrant I

Find:

436. Given: ; is in quadrant II

Find:

437. Given: is in quadrant IV