Material Taken From:

Mathematicsfor the international student

Mathematical Studies SL

Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce

Haese and Haese Publications, 2004

Objectives

• To solve word problems using trigonometry.• To find missing values in 3-dimensioinal

shapes.

Chapter 10 – Section C: Word Problems

1) Find the height of a tree which casts a shadow of 12.4 meters when the sun makes an angle of 52° to the horizon.

2) An A-frame house has the shape of an isosceles triangle with base angles of 70. The oblique walls of the building are

12 meters long. How wide is the building at ground level?

Angles of Depression and Elevation

Angles of Depression and Elevation

3) From a vertical cliff 80 meters above sea level, a fishing boat is observed at an angle of depression

of 6°. How far out to sea is the boat?

4) Find the angle of elevation from a bench to the top of an 80 meter high building if the bench is 105

meters from the foot of the building.

5) The angle of depression from the roof of a building A to the foot of a second building B across the same street and 40 meters away is 65°. The angle of elevation of the

roof of building B to the roof of building A is 35°. How tall is building B?

6) From a window, 29.6 meters above the ground, the angle of elevation of the top of a building is

42°, while the angle of depression to the foot of the building is 32°. Find the height of the building.

7) Ingrid measures the angle of elevation from a point on level ground to the top of a building 120 meters

high to be 32°. She walks towards the building until the angle of elevation is 45°. How far does she walk?

8) A builder designs a roof structure as illustrated. The pitch of the roof is the angle that the roof makes

with the horizontal. Find the pitch of the roof.

9) A cube has sides of length 12 cm. Find the angle between the diagonal AB and one of the edges at B.

Chapter 10 – Section E: 3-D Word Problems

10) Find the angle that: a) PV makes with QV b) SU makes with SQ

11) Find the angle between DG and the base plane EFGH.

12) The given figure shows a square-based pyramid with apex directly above the center of its base.

The base is 10m by 10m and its slant edges are 14 m long.

Find:

a) The length of MCb) The angle that NC makes

with the base ABCD

13) A symmetric square-based pyramid has base lengths of 6 cm and a height of 8 cm as shown.

Find the measure of:a) angle TNMb) angle TRM

Homework

• 10C, page 329–#1, 5, 6, 9, 11, 14

• 10E.1, page 333–#1, 3, 5

• 10E.3, page 336–#2, 4, 5