Right Triangle Trigonometry

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 

Find the length of side y.

• 22.32 cm

• 36.5 cm

• 76.34 cm

• 87.76 cm

Solve for x. Round to the nearest tenth.

• 103.5

• 4.7

• 55.0

• 23.4

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 

Solve for x. Round to the nearest tenth.

• 9.8

• 0.1

• 0.038

• 9.9

Find the measure of the indicated angle.

Choose the correct ratio.

• sin(37)=x/14

• cos(37)=x/14

• tan(37)=x/14

• sin(37)=14/x

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 16 foot ladder leans against a building.  If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

• 39.6

• 6.0

• 14.8

• 13.6