Trigonometry: Tangent Of An Angle, word problems

1. Write the trigonometric ratio tan for the given triangle.

2. Find QR.

Warm up!

P

R Q

16.7

10 cm

o

Tan = opp.= QR adj. PQ

QR= x= 10x tan 16.7= 3.00cm

Different kind of angles from the point of view of a person

Angle of elevation Angle of depression

Zahra is 2o m from a base of a tree which is standing on level ground. From A the angle of elevation of the top C, of the tree is 23.

What is the height of the tree?

o

20 cm(adjacent)

23

C

B A

H m(opposite

)

Tan 23= opp./ adj. = h/20 h/20= 0.4244…. h= 0.4244…x20 h= 8.489 The height of the tree is 8.49m -corrected to

3 s.f.-

Zahra is 2o m from a base of a tree which is standing on level ground. From A the angle of elevation of the top C, of the tree is 23.

What is the height of the tree?

1. Adam is standing on a cliff that is 50 meters high. He looks down at an angle of 30° and sees a boat on the water. How far away is the boat from the foot of the cliff?

2. A park ranger is standing at the top of a 150 foot tower. Looking down at a 15° angle, he sees a forest fire. What is the distance of the fire from the base of the tower?

3. If Abeer is standing 20 meters from the base of a tower, and she is looking up at the top at an angle of 60°, what is the height of the tower?

On your own