Applications of Right Triangles

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 ramp is being built next to a 4-inch high sidewalk. The ramps angle of inclination is 10 degrees.  Estimate the length of the ramp to the nearest tenth of an inch. 

• 4.1 inches
• 3.9 inches
• 22.7 inches 
• 0.7 inches 

A yacht is anchored 90 feet offshore from the base of a lighthouse.  The angle of elevation from the boat to the top of the lighthouse is 26 degrees.  The distance between the yacht and the top of the lighthouse is about 100 feet.  Which of these is nearest to the height of the lighthouse? 

• 25 feet
• 45 feet 
• 110 feet 
• 135 feet 

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 

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 your answer to the nearest degree.  

• 19 degrees
• 45 degrees
• 71 degrees
• 138 degrees 

Solve for the missing angle.

• 50.5 degrees
• 12.7 degrees
• 36.9 degrees
• 72.2 degrees

If you are standing 30 ft away from a 22 foot tree, what is the angle of elevation from where you are standing to the top of the tree.

• 71.9 degrees

• 48.1 degrees

• 523.7 degrees

• 36.3 degrees

A 12 ft ladder is leaning against a wall, making a 50 degree angle with the ground. If the ladder needs to reach one foot higher up the wall, by how many degrees do you need to increase the angle?

• 15.1 degrees

• 8.2 degrees

• 11.1 degrees

• 9.4 degrees

From the top of a 200 foot lighthouse, the angle of depression to a ship on the ocean is 23 degrees . How far is the ship from the base of the lighthouse?

• 471.14 feet

• 84.89 feet

• 511.86 feet

• 217.27 feet