第3章数学モデル

The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle.

The playground at a shopping mall is a triangle with perimeter 48 feet. The lengths of two sides are 19 feet and 14 feet. How long is the third side?

A triangular road sign has base 30 inches and height 40 inches. What is its area?

What is the height of a triangle with area 67.5 square meters and base 9 meters?

One angle of a triangle is $30\text{°}$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.

One angle of a right triangle measures $58\text{°}.$ What is the measure of the other angles of the triangle?

The measure of the smallest angle in a right triangle is $45\text{°}$ less than the measure of the next larger angle. Find the measures of all three angles.

The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more than the smallest side. The third side is six feet more than twice the smallest side. Find the lengths of all sides.

Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is 8 feet tall and Sergio has 10 feet of wire. How far from the base of the antenna can he attach the wire?

Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

The length of a rectangle is 36 feet and the width is 19 feet. Find the ⓐ perimeter ⓑ area.

A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long. Find the ⓐ perimeter ⓑ area.

The area of a rectangle is 2356 square meters. The length is 38 meters. What is the width?

The width of a rectangle is 45 centimeters. The area is 2,700 square centimeters. What is the length?

The length of a rectangle is 12 cm more than the width. The perimeter is 74 cm. Find the length and the width.

The width of a rectangle is three more than twice the length. The perimeter is 96 inches. Find the length and the width.

When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa 2 hours to drive the same distance. Elsa’s speed is seven miles per hour faster than Gabe’s speed. Find Gabe’s speed and Elsa’s speed.

Louellen and Tracy met at a restaurant on the road between Chicago and Nashville. Louellen had left Chicago and drove 3.2 hours towards Nashville. Tracy had left Nashville and drove 4 hours towards Chicago, at a speed one mile per hour faster than Louellen’s speed. The distance between Chicago and Nashville is 472 miles. Find Louellen’s speed and Tracy’s speed.

Two busses leave Amarillo at the same time. The Albuquerque bus heads west on the I-40 at a speed of 72 miles per hour, and the Oklahoma City bus heads east on the I-40 at a speed of 78 miles per hour. How many hours will it take them to be 375 miles apart?

Kyle rowed his boat upstream for 50 minutes. It took him 30 minutes to row back downstream. His speed going upstream is two miles per hour slower than his speed going downstream. Find Kyle’s upstream and downstream speeds.

At 6:30, Devon left her house and rode her bike on the flat road until 7:30. Then she started riding uphill and rode until 8:00. She rode a total of 15 miles. Her speed on the flat road was three miles per hour faster than her speed going uphill. Find Devon’s speed on the flat road and riding uphill.

Anthony drove from New York City to Baltimore, a distance of 192 miles. He left at 3:45 and had heavy traffic until 5:30. Traffic was light for the rest of the drive, and he arrived at 7:30. His speed in light traffic was four miles per hour more than twice his speed in heavy traffic. Find Anthony’s driving speed in heavy traffic and light traffic.