Topic 8 Review Spring 2021

Special Right TrianglesGive answers in reduced radical form.

100

Find v and u. 

v=5 

u=5

200

Find m and n. 

m = 6

n=

2sqrt(3)

300

Find u and v.

u = 

16sqrt(3)/3

v = 

8sqrt(3)/3

400

x = y = 

5sqrt(2)/2

Find a Side

100

Solve for x. Round to the nearest hundredth. 

Sin 25 = x/17

x= (Sin 25)(17)

X= 7.18

200

Find x. Round to the nearest hundredth.

Cos 39 = 20/x

x= 20/Cos 39

x = 25.74

300

Find x. Round to the nearest hundredth.

Tan 47 = x/12

x=(Tan 47)(12)

x= 12.87

400

Suppose a plane is at an altitude of 3500 ft and the angle of elevation from the airport to the plane is 29°. What is the horizontal distance between the plane and the airport? Round to the nearest foot.

Tan 29 = 3500/x

x=3500/(Tan 29)

x = 6314 feet

Find an Angle

100

Find the angle measure. Round to the nearest degree.

Sin X = 29/55

Sin^-1(29/55) = X

X = 32^o

200

Find the angle measure, round to the nearest degree.

Tan X = 15/16

Tan^-1(15/16) = X

43^o

300

Find the angles measure, round to the nearest degree. 

Cos X = 18/30

Cos^-1(18/30) = X

X = 53^o

400

A 15 meter pole is resting on a wall. The base of the pole is 10 meters from the wall. Find the angle the pole makes to the ground. Round to the nearest degree. 

Cos X = 10/15

Cos^-1(10/15) = X

X = 48^o

Smorgasbord

100

Solve for x & y. 

y = 3

x = 

3sqrt(3)

200

An eagle is flying over a clover field looking for its prey. It notices a mouse in the grass below. If the angle of depression to the mouse is 65^o and the eagle is 100 ft. in the air, how far is it from the eagle's eye directly to the mouse? Round to the nearest foot. 

300

A child who is 4 feet tall is standing 200 feet away from the center of the base of the tower. If the child's angle of elevation from their sight is 75^o to see the top of the tower, how tall is the tower?

Find the height of the tower from the child's eyes to top of tower.

Tan 75 = a/200

a = (Tan75)(200)

a = 746.41

Now add in their height for the full height of the tower.

4+746=750 feet 

The tower is about 750 feet.

400

A woman is standing 12 ft. from a sculpture. The angle of elevation from her eye to the top of the sculpture is 30^o and the angle of depression to it's base is 22^o. How tall is the sculpture to the nearest foot?