Geometry Word Problems

Susan is flying a kite, which gets caught in the top of a tree.  Use the diagram to estimate the height of the tree. 

• 63 ft

• 65 ft

• 74 ft

• 87 ft

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree.  The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse? 

• 7.5 ft 

• 15 ft 

• 26 ft 

• 30 ft 

Spencer is going snowboarding.  He rode the ski lift to the top of the mountain, which is at an altitude of 1500 feet.  The angle of elevation from the bottom to the top of the mountain is 25^o.  What is the length of the Spencer’s run (his trip down the hill)? 

• 3216.76 feet

• 633.93 feet

• 699.46 feet

• 3549.30

Sally is flying a kite at an angle of 41 degrees. If the kite is 10 feet up in the air, how long is the kite string?

• 6.6 feet

• 10.3 feet

• 15.2 feet

• 20 feet

Which trigonometric function would you use to find "h", the height of the tree?

• sine

• cosine

• tangent

• none of these

A 30 ft. wire stretches from the top of a light pole diagonally to the ground. The light pole is 10 feet high. What is the angle the wire makes with the ground? Round to the nearest whole degree.

• 66 degrees

• 80 degrees

• 30 degrees

• 19 degrees

A boat is 600 metres from the base of a cliff. Erika, who is sitting in the boat, notices that the angle of elevation to the top of the cliff is 32°. How high is the cliff?

(Round to the nearest tenth. Only the number, no units)

The height of a building is 250 feet. What is the angle of elevation from a point on the level ground 200 feet away from the building?

(Round to the nearest tenth. Only the number, no units)

You are on a ship at sea. You see a lighthouse in the distance. You know the lighthouse is 175 feet tall. You measure the angle of elevation to the top of the lighthouse at 5^o. How far are you from the bottom of the lighthouse?

• 2000.3 feet

• 2007.3 feet

• 1997.9 feet

• 2134.8 feet

You are attacking an enemy castle. Your strategy is to go over the castle wall. You are 1500 meters away from the bottom of the wall. You measure the angle of elevation to the top of the wall at 3^o. How tall is the enemy castle wall?

• 78.6 meters

• 1498.0 meters

• 78.5 meters

• 75.3 meters