Applications of Right Triangle

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

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?

• 14

• 10

• 5.3

• 2

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 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 

A ladder 6 feet long leans against a wall and makes an angle of 71º with the ground.  Find to the nearest tenth of a foot how high up the wall the ladder will reach.

• 2.0 ft

• 3.5 ft

• 5.7 ft

• 6.0 ft

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 

What trigonometric ratio would be used to find the distance from the ship to the plane?

• sine

• cosine

• tangent

• inverse sine

Which scenario describes the picture shown?

• 5 foot ramp is 8 feet away from a building.  What is the angle that the ramp makes with the ground?

• 5 foot ramp leans against an 8 foot structure.  What is the angle that the ramp makes with the ground?

• An 8 foot ramp leans
  against a building 5 feet away.  What angle does the ramp make with the ground?

• 5 foot man is 8 feet away from a building.  What is the angle of elevation?