5-4 Applying Trigonometric Functions

If J=50° and j=12, find r.

G

12 r

50° R g J

Sin 50⁰=12/r.7660=12/r.7660r=12r=15.67

If the angle that the rope makes with the level ground is 52°15’, how long is the rope?

sin 52°15’ = 40/r

The chair lift at a ski resort rises at an angle of 20.75° and attains a vertical height of 1200 feet.

• How far does the chair lift travel up the side of the mountain?

• sin 20.75°=1200/d• .3543=1200/d• .3543d=1200• d=3387.0 ft

d1200

20.75°

• A film crew in a helicopter records an overhead view of a skier’s downhill run from where she gets off the chair lift at the top to where she gets back on the chair lift for her next run. If the helicopter follows a level flight path, what is the length of that path.

• About 3167.3 ft

d1200

20.75°

---------------------------------

• A regular pentagon is inscribed in a circle with diameter 8.34 centimeters. The apothem of a regular polygon is the measure of a line segment from the center of the polygon to the midpoint of one of its sides. Find the apothem of the pentagon.

The measure of α is 360⁄ 10 or 36°

• A regular hexagon is inscribed in a circle with diameter 26.6 centimeters. Find the apothem of the hexagon.

• About 11.5 cm

Angle of elevation – the angle between a horizontal line and the line of sight from an observer to an object at a higher level.Angle of depression – angle to an object at a lower angle.

• An observer in the top of a lighthouse determines that the angles of depression to two sailboats directly in line with the lighthouse are 3.5° and 5.75°. If the observer is 125 feet above sea level, find the distance between the boats.

125

• John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º . How tall is the tree?

• A building is 50 feet high. At a distance away from the building, an observer notices that the angle of elevation to the top of the building is 41º. How far is the observer from the base of the building?

• An airplane is flying at a height of 2 miles above the ground. The distance along the ground from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to the airport?

• A bird sits on top of a lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is . The distance from the bird to the observer is 25 meters. How tall is the lamppost?

• A man who is 2 m tall stands on horizontal ground 30 m from a tree. The angle of elevation of the top of the tree from his eyes is 28˚. Estimate the height of the tree.

• From a point 80 meters from the base of a building to the top of the building the angle of elevation is 51°. From the same point to the top of a flag staff on the building the angle of elevation is 54°.