30 60 90 Right Triangle Word Problems

If you place a 39-foot ladder against the top of a building and the bottom of the ladder is 33 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.

• 51.1

• 20.8

• 432

• 2160

A 13 ft. ladder is leaning against the house. The top of the ladder touches the house at 10 feet above the ground. How far away is the bottom of the ladder from the house?

• 10 feet

• 7.5 feet

• 8.3 feet

• 3.8 feet

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 closest 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 

• 17 ft 

I have been given the long leg in this 30-60-90 triangle.  How do I find the short leg?

• Multiply 7 by 2

• Multiply 7 by √3

• Divide 7 by 2

• Divide 7 by √3

What is the value of x? Value only, no x =

Mathematical Equivalence

ON

I have been given the short leg in this 30-60-90 triangle.  How do I find the length of the hypotenuse?

• Multiply 4 by 2

• Multiply 4 by √3

• Multiply 4 by √2

• Divide 4 by √3

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. How many degrees should the tourist tilt his camera down to photograph the deer? Round your answer to the nearest degree.

• 19 degrees

• 45 degrees

• 71 degrees

• 138 degrees

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

• 63.6 ft

• 1.59 ft

• 74.2 ft

• 86.9 ft

The top of a ladder is leaning against a vertical wall, 12 feet above the floor. The bottom of the ladder is resting on the floor, 9 feet from the base of the wall. How long is the ladder?

• 15 feet

• 17 feet

• 19 feet

• 21 feet