Name: ______Date: ______

Geometry A U7D5 Modeling with Trig - Identifying the Tools Needed to Solve

Draw a labeled diagram to represent the problem. Identify the type of problem. Then solve the problem using the method that matches that type.

1) A ladder leaning against a building makes an angle of 65° with the ground and reaches a point on the building 20 feet above the ground. What is the length of the ladder to the nearest foot?

2) A wire stretches from the top of an 11 foot pole to a stake in the ground that is 5 feet from the foot of the pole. Find the length of the wire to the nearest tenth of a foot.

3) A wooden beam 24 feet long leans against a wall and makes an angle of 71° with the ground. How high up the wall does the beam reach to the nearest foot?

4) A 28-foot ladder is leaning against the wall. If the foot of the ladder is 12 feet from the building, find to the nearest degree the angle the ladder makes with the ground.

5) An airplane climbs at an angle of 13° with the ground. What is the distance it has traveled (to the nearest hundred feet) when it has attained an altitude of 400 feet?

6) A six-foot-tall person is standing next to a flagpole. The person is casting a shadow feet in length while the flagpole is casting a shadow 5 feet in length. How tall is the flagpole?

7) A straight road to the top of a hill is 2,500 feet long and makes an angle of 12° with the horizontal. What is the height of the hill to the nearest foot?

8) A guy wire attached to the top of a pole reaches a stake in the ground 26 feet from the foot of the pole and makes an angle of 48° with the ground. What is the length of the guy wire to the nearest foot?

9) Each step in a staircase has a 7-inch rise and a 12-inch run. Find to the nearest degree the angle the staircase makes with the ground.

10) The Rivera family bought a new tent for camping. Their old tent is triangular with two equal sides of 10 feet and a floor width of 15 feet.If the new tent is similar in shape to the old tent and has equal sides of 16 feet, how wide is the floor of the new tent?

11) A kite that has been secured to a stake in the ground with a 20-foot string. The kite is located 12 feet from the ground, directly over point X. What is the distance along the ground, in feet, between the stake and point X? [Show all work.]