A firefighter placed a 25-foot ladder against the side of a house. The top of the ladder is 20 feet above the ground, as shown below.

What is the distance (x) between the base of the ladder and the house?

Ralph and Sara built the ramp shown below for a skateboard competition.

What is the angle of elevation (x) of the ramp? Round the answer to the nearest degree.

A roof support is shown below.

Which of these equations should be used to find the height (x) of the support?

A cat is stuck in a tree as shown below. The firefighter places a ladder at a 20° angle with the tree. The ladder is 20 feet long.

How high (h), in feet, is the cat above the ground?

The area of the rectangle shown below is 168 square feet.

What is the length, in feet, of the diagonal?

John designed a system of pulleys to lift wooden boards, as shown below.

To what maximum height (x) will his system of pulleys lift the boards? Round the answer to the nearest meter.

A ladder leaning against a house is shown below.

What is the distance (x) from the base of the ladder to the house? Round the answer to the nearest foot.

A lighthouse, which is 18 feet high, stands on a cliff that is 150 feet above sea level. The distance from the top of the lighthouse to a sailboat on the ocean is 360 feet.

What is the angle of elevation (x) from the sailboat to the top of the lighthouse? Round the answer to the nearest degree.

A regular polygon has 20 sides. What is the measure of each interior angle?

An airplane makes a 15° angle of elevation from the runway when it takes off. The airplane pictured below is 2,000 feet along the ground from its take-off point.

At what height (h) is the airplane? Round the answer to the nearest foot.

The Warren Truss shown below consists of 14 congruent right triangles. The distance from point X to point Y is 30 feet and the distance from point Y to point Z is 12 feet.

What is the height (h) of the truss? Round the answer to the nearest foot.

One of the support wires for a radio tower is 100 feet long. One end of the wire is 40 feet from the base of the tower, as shown in the diagram below.

What angle (x), in degrees, does the support wire make with the ground?

A school is purchasing trim to go around all four edges of the banner shown below.

How many inches of trim should be purchased?

In the diagram below, the radius of circle S is 10 units.

What is the length of  ?

A spotlight shines on the front of a building. The spotlight is 45 feet from the front of the building and shines on a point 27 feet above the ground.

What is the measure of the angle (x) that the spotlight forms with the ground? Round the answer to the nearest degree.

A 30-foot ladder is placed so that the base of the ladder is 11 feet from the side of the building.

What is the measure of the angle (x) where the ladder meets with the ground? Round the answer to the nearest degree.

From a tower 60 feet above the water's edge, the line of sight to a sailboat makes an 83.5° angle with the tower.

What is the distance (x) from the base of the tower to the sailboat?

The perimeter of a square is 52 feet. What is the length of the diagonal of the square? Round the answer to the nearest foot.

Diagonals of a regular hexagon were drawn to form equilateral triangles, isosceles triangles, and a smaller regular hexagon.

What is the measure, in degrees, of angle x?

A television store advertises a sale on 30-inch televisions. The ad says the screen is a rectangle that is 18 inches tall, but the ad does not mention the width.

What is the width of the television screen?

Triangle ABC is shown below.

What is the area, in square meters, of ?

Right triangle JKL is shown below.

What is the measure of ? Round the answer to the nearest degree.

The escalator shown below is 109 feet long and makes an angle of 10° with the floor.

Which trigonometric ratio should be used to find the height () of the escalator?

From a point 125 feet from the base of a building, the angle of elevation from the ground to the top of the building is 50°.

What is the height () of the building? Round the answer to the nearest foot.

A lamp points toward the base of a doorway as shown below.

What is the height, in feet, of the lamp?

Look at the diagram below.

What is the length of WX ?

Johnny wants to build a 15-foot sloped roof at an angle of 43°, as shown in the diagram below.

What is the height (h) of the beam that is needed to support the roof? Round the answer to the nearest foot.

In the diagram below, NP is tangent to circle O.   NP = 24 and OP = 25.

What is the length of the diameter of circle O?

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet.

At what angle (x) should the tourist hold his camera to photograph the deer? Round the answer to the nearest degree.

An object dropped from the top of the Leaning Tower of Pisa lands 17 feet from the base.

Which of these equations should be used to determine the angle (x) that the Leaning Tower of Pisa makes with the ground?

Sections of pipe are connected as shown below.

What is the length (x), in feet, of the section of pipe connecting point A to point B?

A jeweler designed a piece of jewelry using congruent pieces of silver. The pieces are evenly spaced except for a 90° open space at the bottom.

What is the measure of x? Round the answer to the nearest degree.

A machinist is making the stop sign shown below by cutting a regular octagon from a square piece of metal.

What is the measure of angle 1?

Look at the figure below.

What is the measure, in degrees, of angle C?

Two people leave from the same point. One travels 12 meters north. The other travels 9 meters east. How far apart are they?

A shelf and bracket are shown below. The shelf is perpendicular to the wall.

Note: This figure is not drawn to scale.

What angle (x), in degrees, does the bracket make with the wall?

Two wires support a young tree as shown below.

Note: This figure is not drawn to scale.

What is the length, in meters, of each wire?

A trapezoid is shown below.

Note: The figure is not drawn to scale.

What is the missing length (x)? Round the answer to the nearest inch.

A diagram of a baseball field is shown below. The infield is a square that measures 90 feet on each side.

Note: The figure is not drawn to scale.

A player threw a ball from point P to third base. How far did the player throw the ball? Round the answer to the nearest foot.

A local airport needs to know the height of the cloud ceiling to determine if planes can take off or land. To find the height (x) of the cloud ceiling at night, a spotlight is turned on and directed straight up to light the base of the clouds. Radar is used to measure the angle of elevation to the base of the clouds.

Note: The figure is not drawn to scale.

What is the height (x) of the cloud ceiling? Round the answer to the nearest meter.

A construction worker is building the roof for a doghouse, as shown in the picture below. He is using 8-foot boards to build the slanted part of the roof. The doghouse is 10 feet wide.

Note: The figure is not drawn to scale.

What is the measure of angle K? Round the answer to the nearest degree.

Each interior angle of a regular polygon measures 168°. How many sides does the polygon have?

In the game of baseball, home plate is shaped like a pentagon, as shown below. Three of the angles are 90° angles, and the other two angles are congruent to each other.

What is the measure (x) of each of the other two angles?

The mainsail of a boat is shown below.

What is the length, in feet, of AB?