1. Measuring Angles

Concept Check Classify each triangle as acute, right, or obtuse. Also classify each as equilateral, isosceles, or scalene. See the discussion following Example 2.

Convert each radian measure to degrees. See Examples 2(a) and 2(b). 15π

Find the unknown side lengths in each pair of similar triangles. See Example 4.

Solve each problem. See Example 5. Height of a Lighthouse The Biloxi lighthouse in the figure casts a shadow 28 m long at 7 A.M. At the same time, the shadow of the lighthouse keeper, who is 1.75 m tall, is 3.5 m long. How tall is the lighthouse?

Solve each problem. See Example 5. Height of a Building A house is 15 ft tall. Its shadow is 40 ft long at the same time that the shadow of a nearby building is 300 ft long. Find the height of the building.

Solve each problem. See Example 5. Height of a Carving of Lincoln Assume that Lincoln was 6 1/3 fttall and his head was 3/4 ftlong. Knowing that the carved head of Lincoln at Mt. Rushmore is 60 ft tall, find how tall his entire body would be if it were carved into the mountain.

In Exercises 65–66, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in centimeters. In each exercise, find: a. the maximum displacement b. the frequency c. the time required for one cycle.d = 20 cos π/4 t

In each figure, there are two similar triangles. Find the unknown measurement. Give approximations to the nearest tenth.

In Exercises 67–68, an object is attached to a coiled spring. In Exercise 67, the object is pulled down (negative direction from the rest position) and then released. In Exercise 68, the object is propelled downward from its rest position. Write an equation for the distance of the object from its rest position after t seconds.

Solve each problem. Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum distance from Earth's surface of about 94,500,000 mi. The moon has a smaller diameter of 2159 mi. For a total solar eclipse to occur, the moon must pass between Earth and the sun. The moon must also be close enough to Earth for the moon's umbra (shadow) to reach the surface of Earth. (Data from Karttunen, H., P. Kröger, H. Oja, M. Putannen, and K. Donners, Editors, Fundamental Astronomy, Fourth Edition, Springer-Verlag.) a. Calculate the maximum distance, to the nearest thousand miles, that the moon can be from Earth and still have a total solar eclipse occur. (Hint: Use similar triangles.)

Solar Eclipse on Neptune (Refer to Exercise 69.) The sun's distance from Neptune is approximately 2,800,000,000 mi (2.8 billion mi). The largest moon of Neptune is Triton, with a diameter of approximately 1680 mi. (Data fromThe World Almanac and Book of Facts.) b. Triton is approximately 220,000 mi from Neptune. Is it possible for Triton to cause a total eclipse on Neptune?

Solar Eclipse on Mars (Refer to Exercise 69.) The sun's distance from the surface of Mars is approximately 142,000,000 mi. One of Mars' two moons, Phobos, has a maximum diameter of 17.4 mi. (Data fromThe World Almanac and Book of Facts.) b. Phobos is approximately 5800 mi from Mars. Is it possible for Phobos to cause a total eclipse on Mars?

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 30°

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 45°

Find the measure of each marked angle. See Example 2.